Class 9 Algebraic Identities — practice questions with answers

Polynomials · 5 sample questions from the school syllabus. Try each one, then open the answer and the worked solution.

1. Expand

(x + 3)^{2}

A $x^{2} + 6 x + 6$
B $x^{2} + 6 x + 9$
C $x^{2} + 9$
D $x^{2} + 3 x + 9$

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Answer: B)

x^{2} + 6 x + 9

(a + b)^{2} = a^{2} + 2 ab + b^{2}

x^{2} + 2 (x) (3) + 9 = x^{2} + 6 x + 9

. Leaving out the middle term 6x is the most common slip.

2. Find

5 1^{2} - 4 9^{2}

quickly.

A100
B200
C400
D2

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Answer: B) 200

a^{2} - b^{2} = (a + b) (a - b) = (100) (2) = 200

3. From the figure, the shaded region is a square of side a with a square of side b removed. If a = 15 and b = 5, find the shaded area using an identity.

A200 sq units
B100 sq units
C150 sq units
D250 sq units

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Answer: A) 200 sq units

Shaded area =

a^{2} - b^{2} = (a + b) (a - b) = 20 \times 10 = 200

. (100 is

(a - b)^{2}

4. Given that

a + b + c = 0

, what is

a^{3} + b^{3} + c^{3}

equal to?

A $(a + b + c)^{3}$
B $3 ab c$
C $ab c$
D $0$

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Answer: B)

3 ab c

a^{3} + b^{3} + c^{3} - 3 ab c = (a + b + c) (a^{2} + b^{2} + c^{2} - ab - b c - c a)

. With a + b + c = 0 the right side is 0, so the sum of cubes is 3abc.

5. If

x + y + z = 9

and

x y + yz + z x = 26

, find

x^{3} + y^{3} + z^{3} - 3 x yz

A27
B261
C−153
D9

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Answer: A) 27

First

x^{2} + y^{2} + z^{2} = 81 - 52 = 29

. Then

x^{3} + y^{3} + z^{3} - 3 x yz = (x + y + z) (x^{2} + y^{2} + z^{2} - x y - yz - z x) = 9 (29 - 26) = 27

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