Grade 9 : Mathematics - 9. Algebraic Identities (Set 1)

Question 1

Expand the expression $(x + 5)^2$ using a suitable algebraic identity.

Accepted Answer

A) $x^2 + 10x + 25$

Answer

B) $x^2 + 5x + 25$

Answer

C) $x^2 + 10x + 10$

Answer

D) $x^2 + 25$

Question 2

Expand the expression $(2a - 3b)^2$ using algebraic identities.

Accepted Answer

B) $4a^2 - 12ab + 9b^2$

Answer

A) $4a^2 - 6ab + 9b^2$

Answer

C) $4a^2 + 12ab + 9b^2$

Answer

D) $2a^2 - 12ab + 3b^2$

Question 3

Evaluate the numerical product $103 imes 107$ without direct multiplication.

Accepted Answer

C) 11021

Answer

A) 11000

Answer

B) 10921

Answer

D) 11121

Question 4

Factorise the expression $x^2 - 16y^2$.

Accepted Answer

A) $(x - 4y)(x + 4y)$

Answer

B) $(x - 16y)(x + y)$

Answer

C) $(x - 4y)^2$

Answer

D) $(x + 4y)^2$

Question 5

Find the product $(x + 4)(x + 10)$ using the standard identity $(x + a)(x + b) = x^2 + (a + b)x + ab$.

Accepted Answer

D) $x^2 + 14x + 40$

Answer

A) $x^2 + 14x + 14$

Answer

B) $x^2 + 40x + 14$

Answer

C) $x^2 + 10x + 40$

Question 6

Expand the trinomial square $(a + 2b + 3c)^2$.

Accepted Answer

B) $a^2 + 4b^2 + 9c^2 + 4ab + 12bc + 6ca$

Answer

A) $a^2 + 4b^2 + 9c^2 + 2ab + 6bc + 3ca$

Answer

C) $a^2 + 2b^2 + 3c^2 + 4ab + 12bc + 6ca$

Answer

D) $a^2 + 4b^2 + 9c^2 + 4ab + 6bc + 6ca$

Question 7

If $x + \frac{1}{x} = 6$, find the value of $x^2 + \frac{1}{x^2}$.

Accepted Answer

C) 34

Answer

A) 38

Answer

B) 36

Answer

D) 32

Question 8

Expand $(2x + 1)^3$ using the algebraic identity for the cube of a binomial.

Accepted Answer

A) $8x^3 + 12x^2 + 6x + 1$

Answer

B) $8x^3 + 6x^2 + 6x + 1$

Answer

C) $8x^3 + 12x^2 + 3x + 1$

Answer

D) $6x^3 + 12x^2 + 6x + 1$

Question 9

Expand $(x - 3y)^3$.

Accepted Answer

C) $x^3 - 9x^2y + 27xy^2 - 27y^3$

Answer

A) $x^3 - 9x^2y + 9xy^2 - 27y^3$

Answer

B) $x^3 - 27y^3$

Answer

D) $x^3 - 27x^2y + 27xy^2 - 27y^3$

Question 10

Factorise $8x^3 + 27y^3$ using the sum of cubes identity.

Accepted Answer

B) $(2x + 3y)(4x^2 - 6xy + 9y^2)$

Answer

A) $(2x + 3y)(4x^2 + 6xy + 9y^2)$

Answer

C) $(2x - 3y)(4x^2 + 6xy + 9y^2)$

Answer

D) $(8x + 27y)(x^2 - xy + y^2)$

Question 11

Evaluate $99^3$ using algebraic identities.

Accepted Answer

D) 970299

Answer

A) 970199

Answer

B) 980299

Answer

C) 970301

Question 12

If $a + b + c = 0$, what is the value of $a^3 + b^3 + c^3$?

Accepted Answer

A) $3abc$

Answer

B) 0

Answer

C) abc

Answer

D) $-3abc$

Question 13

Compute the value of $28^3 + (-15)^3 + (-13)^3$ without finding individual cubes.

Accepted Answer

C) 16380

Answer

A) -16380

Answer

B) 15380

Answer

D) 0

Question 14

Factorise the expression $x^2 + 6x + 9$.

Accepted Answer

B) $(x + 3)^2$

Answer

A) $(x - 3)^2$

Answer

C) $(x + 9)(x + 1)$

Answer

D) $(x + 6)(x + 3)$

Question 15

If $x - \frac{1}{x} = 4$, find the value of $x^2 + \frac{1}{x^2}$.

Accepted Answer

A) 18

Answer

B) 14

Answer

C) 16

Answer

D) 20

Question 16

Factorise $27x^3 - y^3$ using the difference of cubes identity.

Accepted Answer

D) $(3x - y)(9x^2 + 3xy + y^2)$

Answer

A) $(3x - y)(9x^2 - 3xy + y^2)$

Answer

B) $(3x + y)(9x^2 - 3xy + y^2)$

Answer

C) $(3x - y)(3x^2 + 3xy + y^2)$

Question 17

Expand $(x - 2y - 3z)^2$.

Accepted Answer

C) $x^2 + 4y^2 + 9z^2 - 4xy + 12yz - 6zx$

Answer

A) $x^2 + 4y^2 + 9z^2 - 4xy - 12yz - 6zx$

Answer

B) $x^2 - 4y^2 - 9z^2 - 4xy + 12yz - 6zx$

Answer

D) $x^2 + 4y^2 + 9z^2 + 4xy + 12yz + 6zx$

Question 18

Find the product $105 imes 95$ using the identity $(a + b)(a - b) = a^2 - b^2$.

Accepted Answer

B) 9975

Answer

A) 9925

Answer

C) 9985

Answer

D) 10025

Question 19

If $x + y = 10$ and $xy = 21$, find the value of $x^2 + y^2$.

Accepted Answer

A) 58

Answer

B) 79

Answer

C) 100

Answer

D) 42

Question 20

Evaluate $a^3 + b^3 + c^3 - 3abc$ given that $a + b + c = 9$ and $ab + bc + ca = 26$.

Accepted Answer

C) 27

Answer

A) 18

Answer

B) 21

Answer

D) 36

Grade 9 : Mathematics - 9. Algebraic Identities (Set 1)