Grade 9 : Mathematics - 9. Algebraic Identities (Set 2)

Question 1

Expand $(x + 4)(x + 7)$ using a suitable algebraic identity.

Accepted Answer

A) $x^2 + 11x + 28$

Answer

B) $x^2 + 28x + 11$

Answer

C) $x^2 + 11x + 11$

Answer

D) $x^2 + 28x + 28$

Question 2

Evaluate $103 imes 107$ directly using algebraic identities without direct multiplication.

Accepted Answer

A) 11021

Answer

B) 11014

Answer

C) 11031

Answer

D) 10021

Question 3

Factorise the expression $49a^2 + 70ab + 25b^2$.

Accepted Answer

B) $(7a + 5b)^2$

Answer

A) $(7a - 5b)^2$

Answer

C) $(7a + 5b)(7a - 5b)$

Answer

D) $(49a + 25b)^2$

Question 4

If $x + \frac{1}{x} = 5$, find the numerical value of $x^2 + \frac{1}{x^2}$.

Accepted Answer

C) 23

Answer

A) 25

Answer

B) 27

Answer

D) 21

Question 5

Expand the trinomial expression $(2x - y + z)^2$.

Accepted Answer

A) $4x^2 + y^2 + z^2 - 4xy - 2yz + 4xz$

Answer

B) $4x^2 - y^2 + z^2 - 4xy - 2yz + 4xz$

Answer

C) $4x^2 + y^2 + z^2 + 4xy - 2yz + 4xz$

Answer

D) $4x^2 + y^2 + z^2 - 2xy - 2yz + 2xz$

Question 6

Evaluate $99^2$ using the identity $(a-b)^2 = a^2 - 2ab + b^2$.

Accepted Answer

A) 9801

Answer

B) 9901

Answer

C) 9701

Answer

D) 9810

Question 7

Factorise $25x^2 - 16y^2$.

Accepted Answer

C) $(5x - 4y)(5x + 4y)$

Answer

A) $(5x - 4y)^2$

Answer

B) $(5x + 4y)^2$

Answer

D) $(25x - 16y)(25x + 16y)$

Question 8

Expand $(3a + 4b)^3$ completely.

Accepted Answer

C) $27a^3 + 108a^2b + 144ab^2 + 64b^3$

Answer

A) $27a^3 + 64b^3$

Answer

B) $27a^3 + 36a^2b + 48ab^2 + 64b^3$

Answer

D) $9a^3 + 108a^2b + 144ab^2 + 12b^3$

Question 9

Evaluate $104^3$ using algebraic identities.

Accepted Answer

A) 1124864

Answer

B) 1124800

Answer

C) 1040000

Answer

D) 1124964

Question 10

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

Accepted Answer

B) $3abc$

Answer

A) abc

Answer

C) 0

Answer

D) $a^2+b^2+c^2$

Question 11

Evaluate $55^3 - 25^3 - 30^3$ without directly calculating the cubes.

Accepted Answer

A) 123750

Answer

B) 125000

Answer

C) 112500

Answer

D) 0

Question 12

Factorise $x^3 + 8y^3 + 27z^3 - 18xyz$.

Accepted Answer

A) $(x + 2y + 3z)(x^2 + 4y^2 + 9z^2 - 2xy - 6yz - 3xz)$

Answer

B) $(x + 2y + 3z)(x^2 + 2y^2 + 3z^2 - xy - yz - xz)$

Answer

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

Answer

D) $(x + 2y + 3z)^3$

Question 13

Find the product $(2x + 3y)(4x^2 - 6xy + 9y^2)$.

Accepted Answer

B) $8x^3 + 27y^3$

Answer

A) $8x^3 - 27y^3$

Answer

C) $4x^3 + 9y^3$

Answer

D) $8x^3 + 18xy + 27y^3$

Question 14

A architect plans a square park with a side length of $(3x + 5)$ meters.

Express the total surface area of the park as a simplified polynomial in terms of $x$.

Accepted Answer

C) $9x^2 + 30x + 25$

Answer

A) $9x^2 + 25$

Answer

B) $9x^2 + 15x + 25$

Answer

D) $6x^2 + 30x + 10$

Question 15

A storage container has dimensions $(x + 2)$ cm, $(x + 3)$ cm, and $(x + 5)$ cm.

Find the simplified polynomial expression representing its volume.

Accepted Answer

A) $x^3 + 10x^2 + 31x + 30$

Answer

B) $x^3 + 10x^2 + 30x + 31$

Answer

C) $x^3 + 30x^2 + 31x + 10$

Answer

D) $x^3 + 10x + 30$

Question 16

If $x - \frac{1}{x} = 4$, find the value of $x^3 - \frac{1}{x^3}$.

Accepted Answer

C) 76

Answer

A) 52

Answer

B) 64

Answer

D) 88

Question 17

If $a + b + c = 9$ and $ab + bc + ca = 26$, find $a^2 + b^2 + c^2$.

Accepted Answer

A) 29

Answer

B) 31

Answer

C) 55

Answer

D) 81

Question 18

Factorise $x^6 - y^6$ completely into linear and quadratic factors.

Accepted Answer

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

Answer

B) $(x-y)^3(x+y)^3$

Answer

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

Answer

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

Question 19

Find the coefficient of $x$ in the expanded form of $(x - 3)(x + 8)$.

Accepted Answer

C) 5

Answer

A) -24

Answer

B) -5

Answer

D) 11

Question 20

Evaluate $\frac{0.87 imes 0.87 imes 0.87 + 0.13 imes 0.13 imes 0.13}{0.87 imes 0.87 - 0.87 imes 0.13 + 0.13 imes 0.13}$.

Accepted Answer

B) 1

Answer

A) 0.74

Answer

C) 0.13

Answer

D) 10

Grade 9 : Mathematics - 9. Algebraic Identities (Set 2)