𝑥 SSC CGL Tier-I/II, CBSE 9–10

Algebra — formula, example and practice

Identities, linear equations and quadratic roots — board plus competitive.

Content type: original worked example. Not labelled as a previous-year question.

Timed GK/quant mock Shortcuts CBSE Class 10 Maths 150 questions

Formula

(a+b)² = a²+2ab+b² · (a−b)² = a²−2ab+b² · a²−b² = (a−b)(a+b)

Letters stand for numbers. Identities turn expansion into a one-line product.

What you should learn here

Quadratic ax²+bx+c=0 has roots [−b ± √(b²−4ac)] / (2a). Discriminant tells you how many real roots.

Worked example

Question. If a+b = 7 and ab = 10, find a²+b².

Solution. a²+b² = (a+b)² − 2ab = 49 − 20 = 29.

Common mistake. Writing (a+b)² as a²+b².

When to use the shortcut. On CBSE papers, show identity steps. On SSC, plug and compute if numbers are small.

Related chapters and tests

Partnership Geometry Percentage Ratio and Proportion All formulas SSC GD mocks SSC CGL mocks

150 important Algebra questions

Original arithmetic practice for this page. Not labelled as previous-year SSC/railway items. Tap an option to mark it. Open “Answer” for the working.

Q. 1बीजगणित

If x + 2 = 4, then x =

Answer / solution

Correct option: B

x = 4−2 = 2.

Q. 2बीजगणित

If 2x + 4 = 10, then x =

Answer / solution

Correct option: A

2x = 6; x = 3.

Q. 3बीजगणित

(5 + 4)² equals

Answer / solution

Correct option: D

a²+2ab+b² = 81.

Q. 4बीजगणित

(6 − 5)² equals

Answer / solution

Correct option: C

a²−2ab+b² = 1.

Q. 5बीजगणित

7² − 6² equals

Answer / solution

Correct option: D

(a−b)(a+b) = 13.

Q. 6बीजगणित

If x + 7 = 14, then x =

Answer / solution

Correct option: C

x = 14−7 = 7.

Q. 7बीजगणित

If 2x + 4 = 20, then x =

Answer / solution

Correct option: A

2x = 16; x = 8.

Q. 8बीजगणित

(10 + 3)² equals

Answer / solution

Correct option: D

a²+2ab+b² = 169.

Q. 9बीजगणित

(3 − 4)² equals

Answer / solution

Correct option: C

a²−2ab+b² = 1.

Q. 10बीजगणित

4² − 5² equals

Answer / solution

Correct option: A

(a−b)(a+b) = -9.

Q. 11बीजगणित

If x + 6 = 12, then x =

Answer / solution

Correct option: A

x = 12−6 = 6.

Q. 12बीजगणित

If 2x + 4 = 16, then x =

Answer / solution

Correct option: B

2x = 12; x = 6.

Q. 13बीजगणित

(7 + 2)² equals

Answer / solution

Correct option: B

a²+2ab+b² = 81.

Q. 14बीजगणित

(8 − 3)² equals

Answer / solution

Correct option: B

a²−2ab+b² = 25.

Q. 15बीजगणित

9² − 4² equals

Answer / solution

Correct option: D

(a−b)(a+b) = 65.

Q. 16बीजगणित

If x + 5 = 10, then x =

Answer / solution

Correct option: B

x = 10−5 = 5.

Q. 17बीजगणित

If 2x + 4 = 12, then x =

Answer / solution

Correct option: D

2x = 8; x = 4.

Q. 18बीजगणित

(4 + 7)² equals

Answer / solution

Correct option: A

a²+2ab+b² = 121.

Q. 19बीजगणित

(5 − 2)² equals

Answer / solution

Correct option: D

a²−2ab+b² = 9.

Q. 20बीजगणित

6² − 3² equals

Answer / solution

Correct option: A

(a−b)(a+b) = 27.

Q. 21बीजगणित

If x + 4 = 8, then x =

Answer / solution

Correct option: C

x = 8−4 = 4.

Q. 22बीजगणित

If 2x + 4 = 8, then x =

Answer / solution

Correct option: D

2x = 4; x = 2.

Q. 23बीजगणित

(9 + 6)² equals

Answer / solution

Correct option: A

a²+2ab+b² = 225.

Q. 24बीजगणित

(10 − 7)² equals

Answer / solution

Correct option: D

a²−2ab+b² = 9.

Q. 25बीजगणित

3² − 2² equals

Answer / solution

Correct option: D

(a−b)(a+b) = 5.

Q. 26बीजगणित

If x + 3 = 6, then x =

Answer / solution

Correct option: C

x = 6−3 = 3.

Q. 27बीजगणित

If 2x + 4 = 18, then x =

Answer / solution

Correct option: D

2x = 14; x = 7.

Q. 28बीजगणित

(6 + 5)² equals

Answer / solution

Correct option: A

a²+2ab+b² = 121.

Q. 29बीजगणित

(7 − 6)² equals

Answer / solution

Correct option: A

a²−2ab+b² = 1.

Q. 30बीजगणित

8² − 7² equals

Answer / solution

Correct option: B

(a−b)(a+b) = 15.

Q. 31बीजगणित

If x + 2 = 4, then x =

Answer / solution

Correct option: B

x = 4−2 = 2.

Q. 32बीजगणित

If 2x + 4 = 14, then x =

Answer / solution

Correct option: C

2x = 10; x = 5.

Q. 33बीजगणित

(3 + 4)² equals

Answer / solution

Correct option: B

a²+2ab+b² = 49.

Q. 34बीजगणित

(4 − 5)² equals

Answer / solution

Correct option: D

a²−2ab+b² = 1.

Q. 35बीजगणित

5² − 6² equals

Answer / solution

Correct option: C

(a−b)(a+b) = -11.

Q. 36बीजगणित

If x + 7 = 14, then x =

Answer / solution

Correct option: C

x = 14−7 = 7.

Q. 37बीजगणित

If 2x + 4 = 10, then x =

Answer / solution

Correct option: A

2x = 6; x = 3.

Q. 38बीजगणित

(8 + 3)² equals

Answer / solution

Correct option: C

a²+2ab+b² = 121.

Q. 39बीजगणित

(9 − 4)² equals

Answer / solution

Correct option: B

a²−2ab+b² = 25.

Q. 40बीजगणित

10² − 5² equals

Answer / solution

Correct option: C

(a−b)(a+b) = 75.

Q. 41बीजगणित

If x + 6 = 12, then x =

Answer / solution

Correct option: A

x = 12−6 = 6.

Q. 42बीजगणित

If 2x + 4 = 20, then x =

Answer / solution

Correct option: A

2x = 16; x = 8.

Q. 43बीजगणित

(5 + 2)² equals

Answer / solution

Correct option: C

a²+2ab+b² = 49.

Q. 44बीजगणित

(6 − 3)² equals

Answer / solution

Correct option: D

a²−2ab+b² = 9.

Q. 45बीजगणित

7² − 4² equals

Answer / solution

Correct option: A

(a−b)(a+b) = 33.

Q. 46बीजगणित

If x + 5 = 10, then x =

Answer / solution

Correct option: B

x = 10−5 = 5.

Q. 47बीजगणित

If 2x + 4 = 16, then x =

Answer / solution

Correct option: B

2x = 12; x = 6.

Q. 48बीजगणित

(10 + 7)² equals

Answer / solution

Correct option: B

a²+2ab+b² = 289.

Q. 49बीजगणित

(3 − 2)² equals

Answer / solution

Correct option: D

a²−2ab+b² = 1.

Q. 50बीजगणित

4² − 3² equals

Answer / solution

Correct option: B

(a−b)(a+b) = 7.

Q. 51बीजगणित

If x + 4 = 8, then x =

Answer / solution

Correct option: C

x = 8−4 = 4.

Q. 52बीजगणित

If 2x + 4 = 12, then x =

Answer / solution

Correct option: D

2x = 8; x = 4.

Q. 53बीजगणित

(7 + 6)² equals

Answer / solution

Correct option: D

a²+2ab+b² = 169.

Q. 54बीजगणित

(8 − 7)² equals

Answer / solution

Correct option: D

a²−2ab+b² = 1.

Q. 55बीजगणित

9² − 2² equals

Answer / solution

Correct option: C

(a−b)(a+b) = 77.

Q. 56बीजगणित

If x + 3 = 6, then x =

Answer / solution

Correct option: C

x = 6−3 = 3.

Q. 57बीजगणित

If 2x + 4 = 8, then x =

Answer / solution

Correct option: D

2x = 4; x = 2.

Q. 58बीजगणित

(4 + 5)² equals

Answer / solution

Correct option: D

a²+2ab+b² = 81.

Q. 59बीजगणित

(5 − 6)² equals

Answer / solution

Correct option: B

a²−2ab+b² = 1.

Q. 60बीजगणित

6² − 7² equals

Answer / solution

Correct option: C

(a−b)(a+b) = -13.

Q. 61बीजगणित

If x + 2 = 4, then x =

Answer / solution

Correct option: B

x = 4−2 = 2.

Q. 62बीजगणित

If 2x + 4 = 18, then x =

Answer / solution

Correct option: D

2x = 14; x = 7.

Q. 63बीजगणित

(9 + 4)² equals

Answer / solution

Correct option: D

a²+2ab+b² = 169.

Q. 64बीजगणित

(10 − 5)² equals

Answer / solution

Correct option: A

a²−2ab+b² = 25.

Q. 65बीजगणित

3² − 6² equals

Answer / solution

Correct option: B

(a−b)(a+b) = -27.

Q. 66बीजगणित

If x + 7 = 14, then x =

Answer / solution

Correct option: C

x = 14−7 = 7.

Q. 67बीजगणित

If 2x + 4 = 14, then x =

Answer / solution

Correct option: C

2x = 10; x = 5.

Q. 68बीजगणित

(6 + 3)² equals

Answer / solution

Correct option: B

a²+2ab+b² = 81.

Q. 69बीजगणित

(7 − 4)² equals

Answer / solution

Correct option: D

a²−2ab+b² = 9.

Q. 70बीजगणित

8² − 5² equals

Answer / solution

Correct option: C

(a−b)(a+b) = 39.

Q. 71बीजगणित

If x + 6 = 12, then x =

Answer / solution

Correct option: A

x = 12−6 = 6.

Q. 72बीजगणित

If 2x + 4 = 10, then x =

Answer / solution

Correct option: A

2x = 6; x = 3.

Q. 73बीजगणित

(3 + 2)² equals

Answer / solution

Correct option: A

a²+2ab+b² = 25.

Q. 74बीजगणित

(4 − 3)² equals

Answer / solution

Correct option: C

a²−2ab+b² = 1.

Q. 75बीजगणित

5² − 4² equals

Answer / solution

Correct option: B

(a−b)(a+b) = 9.

Q. 76बीजगणित

If x + 5 = 10, then x =

Answer / solution

Correct option: B

x = 10−5 = 5.

Q. 77बीजगणित

If 2x + 4 = 20, then x =

Answer / solution

Correct option: A

2x = 16; x = 8.

Q. 78बीजगणित

(8 + 7)² equals

Answer / solution

Correct option: A

a²+2ab+b² = 225.

Q. 79बीजगणित

(9 − 2)² equals

Answer / solution

Correct option: A

a²−2ab+b² = 49.

Q. 80बीजगणित

10² − 3² equals

Answer / solution

Correct option: D

(a−b)(a+b) = 91.

Q. 81बीजगणित

If x + 4 = 8, then x =

Answer / solution

Correct option: C

x = 8−4 = 4.

Q. 82बीजगणित

If 2x + 4 = 16, then x =

Answer / solution

Correct option: B

2x = 12; x = 6.

Q. 83बीजगणित

(5 + 6)² equals

Answer / solution

Correct option: A

a²+2ab+b² = 121.

Q. 84बीजगणित

(6 − 7)² equals

Answer / solution

Correct option: B

a²−2ab+b² = 1.

Q. 85बीजगणित

7² − 2² equals

Answer / solution

Correct option: B

(a−b)(a+b) = 45.

Q. 86बीजगणित

If x + 3 = 6, then x =

Answer / solution

Correct option: C

x = 6−3 = 3.

Q. 87बीजगणित

If 2x + 4 = 12, then x =

Answer / solution

Correct option: D

2x = 8; x = 4.

Q. 88बीजगणित

(10 + 5)² equals

Answer / solution

Correct option: C

a²+2ab+b² = 225.

Q. 89बीजगणित

(3 − 6)² equals

Answer / solution

Correct option: B

a²−2ab+b² = 9.

Q. 90बीजगणित

4² − 7² equals

Answer / solution

Correct option: D

(a−b)(a+b) = -33.

Q. 91बीजगणित

If x + 2 = 4, then x =

Answer / solution

Correct option: B

x = 4−2 = 2.

Q. 92बीजगणित

If 2x + 4 = 8, then x =

Answer / solution

Correct option: D

2x = 4; x = 2.

Q. 93बीजगणित

(7 + 4)² equals

Answer / solution

Correct option: A

a²+2ab+b² = 121.

Q. 94बीजगणित

(8 − 5)² equals

Answer / solution

Correct option: A

a²−2ab+b² = 9.

Q. 95बीजगणित

9² − 6² equals

Answer / solution

Correct option: A

(a−b)(a+b) = 45.

Q. 96बीजगणित

If x + 7 = 14, then x =

Answer / solution

Correct option: C

x = 14−7 = 7.

Q. 97बीजगणित

If 2x + 4 = 18, then x =

Answer / solution

Correct option: D

2x = 14; x = 7.

Q. 98बीजगणित

(4 + 3)² equals

Answer / solution

Correct option: C

a²+2ab+b² = 49.

Q. 99बीजगणित

(5 − 4)² equals

Answer / solution

Correct option: C

a²−2ab+b² = 1.

Q. 100बीजगणित

6² − 5² equals

Answer / solution

Correct option: B

(a−b)(a+b) = 11.

Q. 101बीजगणित

If x + 6 = 12, then x =

Answer / solution

Correct option: A

x = 12−6 = 6.

Q. 102बीजगणित

If 2x + 4 = 14, then x =

Answer / solution

Correct option: C

2x = 10; x = 5.

Q. 103बीजगणित

(9 + 2)² equals

Answer / solution

Correct option: C

a²+2ab+b² = 121.

Q. 104बीजगणित

(10 − 3)² equals

Answer / solution

Correct option: B

a²−2ab+b² = 49.

Q. 105बीजगणित

3² − 4² equals

Answer / solution

Correct option: C

(a−b)(a+b) = -7.

Q. 106बीजगणित

If x + 5 = 10, then x =

Answer / solution

Correct option: B

x = 10−5 = 5.

Q. 107बीजगणित

If 2x + 4 = 10, then x =

Answer / solution

Correct option: A

2x = 6; x = 3.

Q. 108बीजगणित

(6 + 7)² equals

Answer / solution

Correct option: D

a²+2ab+b² = 169.

Q. 109बीजगणित

(7 − 2)² equals

Answer / solution

Correct option: C

a²−2ab+b² = 25.

Q. 110बीजगणित

8² − 3² equals

Answer / solution

Correct option: D

(a−b)(a+b) = 55.

Q. 111बीजगणित

If x + 4 = 8, then x =

Answer / solution

Correct option: C

x = 8−4 = 4.

Q. 112बीजगणित

If 2x + 4 = 20, then x =

Answer / solution

Correct option: A

2x = 16; x = 8.

Q. 113बीजगणित

(3 + 6)² equals

Answer / solution

Correct option: C

a²+2ab+b² = 81.

Q. 114बीजगणित

(4 − 7)² equals

Answer / solution

Correct option: A

a²−2ab+b² = 9.

Q. 115बीजगणित

5² − 2² equals

Answer / solution

Correct option: A

(a−b)(a+b) = 21.

Q. 116बीजगणित

If x + 3 = 6, then x =

Answer / solution

Correct option: C

x = 6−3 = 3.

Q. 117बीजगणित

If 2x + 4 = 16, then x =

Answer / solution

Correct option: B

2x = 12; x = 6.

Q. 118बीजगणित

(8 + 5)² equals

Answer / solution

Correct option: D

a²+2ab+b² = 169.

Q. 119बीजगणित

(9 − 6)² equals

Answer / solution

Correct option: C

a²−2ab+b² = 9.

Q. 120बीजगणित

10² − 7² equals

Answer / solution

Correct option: B

(a−b)(a+b) = 51.

Q. 121बीजगणित

If x + 2 = 4, then x =

Answer / solution

Correct option: B

x = 4−2 = 2.

Q. 122बीजगणित

If 2x + 4 = 12, then x =

Answer / solution

Correct option: D

2x = 8; x = 4.

Q. 123बीजगणित

(5 + 4)² equals

Answer / solution

Correct option: D

a²+2ab+b² = 81.

Q. 124बीजगणित

(6 − 5)² equals

Answer / solution

Correct option: C

a²−2ab+b² = 1.

Q. 125बीजगणित

7² − 6² equals

Answer / solution

Correct option: D

(a−b)(a+b) = 13.

Q. 126बीजगणित

If x + 7 = 14, then x =

Answer / solution

Correct option: C

x = 14−7 = 7.

Q. 127बीजगणित

If 2x + 4 = 8, then x =

Answer / solution

Correct option: D

2x = 4; x = 2.

Q. 128बीजगणित

(10 + 3)² equals

Answer / solution

Correct option: D

a²+2ab+b² = 169.

Q. 129बीजगणित

(3 − 4)² equals

Answer / solution

Correct option: C

a²−2ab+b² = 1.

Q. 130बीजगणित

4² − 5² equals

Answer / solution

Correct option: A

(a−b)(a+b) = -9.

Q. 131बीजगणित

If x + 6 = 12, then x =

Answer / solution

Correct option: A

x = 12−6 = 6.

Q. 132बीजगणित

If 2x + 4 = 18, then x =

Answer / solution

Correct option: D

2x = 14; x = 7.

Q. 133बीजगणित

(7 + 2)² equals

Answer / solution

Correct option: B

a²+2ab+b² = 81.

Q. 134बीजगणित

(8 − 3)² equals

Answer / solution

Correct option: B

a²−2ab+b² = 25.

Q. 135बीजगणित

9² − 4² equals

Answer / solution

Correct option: D

(a−b)(a+b) = 65.

Q. 136बीजगणित

If x + 5 = 10, then x =

Answer / solution

Correct option: B

x = 10−5 = 5.

Q. 137बीजगणित

If 2x + 4 = 14, then x =

Answer / solution

Correct option: C

2x = 10; x = 5.

Q. 138बीजगणित

(4 + 7)² equals

Answer / solution

Correct option: A

a²+2ab+b² = 121.

Q. 139बीजगणित

(5 − 2)² equals

Answer / solution

Correct option: D

a²−2ab+b² = 9.

Q. 140बीजगणित

6² − 3² equals

Answer / solution

Correct option: A

(a−b)(a+b) = 27.

Q. 141बीजगणित

If x + 4 = 8, then x =

Answer / solution

Correct option: C

x = 8−4 = 4.

Q. 142बीजगणित

If 2x + 4 = 10, then x =

Answer / solution

Correct option: A

2x = 6; x = 3.

Q. 143बीजगणित

(9 + 6)² equals

Answer / solution

Correct option: A

a²+2ab+b² = 225.

Q. 144बीजगणित

(10 − 7)² equals

Answer / solution

Correct option: D

a²−2ab+b² = 9.

Q. 145बीजगणित

3² − 2² equals

Answer / solution

Correct option: D

(a−b)(a+b) = 5.

Q. 146बीजगणित

If x + 3 = 6, then x =

Answer / solution

Correct option: C

x = 6−3 = 3.

Q. 147बीजगणित

If 2x + 4 = 20, then x =

Answer / solution

Correct option: A

2x = 16; x = 8.

Q. 148बीजगणित

(6 + 5)² equals

Answer / solution

Correct option: A

a²+2ab+b² = 121.

Q. 149बीजगणित

(7 − 6)² equals

Answer / solution

Correct option: A

a²−2ab+b² = 1.

Q. 150बीजगणित

8² − 7² equals

Answer / solution

Correct option: B

(a−b)(a+b) = 15.

FAQs

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