Factorisation using algebraic identities

Q.

How do you factor $x^2-y^2$?

Q.

Factorise $x^4-625$.

Q.

Factorise: $(25÷4)x^2-y^2÷9$

Q.

Factorise: $27x^3+y^3+z^3-9xyz$

Q. What is the factorised expression for $x^3-27$?

1. $(x+3)(x^2+3x+9)$
2. $(x-3)(x^2-3x+9)$
3. $(x-3)(x^2+3x-9)$
4. $(x-3)(x^2+3x+9)$

Q.

Question 92 (xxi)

Factorise the following using the identity $a^2-b^2=(a+b)(a-b).$

$p^5-16p$

Q.

Factorise: $27x^3+y^3+z^3-9xyz$

Q.

Factors of

$-x^3-125$

1. $(x+5)(x^2-5x+25)$

2. $-1(x+5)(x^2-5x+25)$

3. $(x-5)(x^2+5x-25)$

4. $-1(x-5)(-x^2-5x+25)$

Q. Question 2(viii)
Factorise
$25a^2-4b^2+28bc-49c^2$

Q.

Question 92 (xix)

Factorise the following using the identity $a^2-b^2=(a+b)(a-b).$

$x^4-1$

Q. What is the factorised expression for $x^3-27$?

1. $(x-3)(x^2+3x+9)$
2. $(x+3)(x^2+3x+9)$
3. $(x-3)(x^2-3x+9)$
4. $(x-3)(x^2+3x-9)$

Q.

Question 92 (iv)

Factorise the following using the identity $a^2-b^2=(a+b)(a-b).$

$3a^2{b}^3-27a^{4}b$

Q.

Factorize $25x^2+4y^2+9z^2-20xy-12yz+30xz$

Q.

What is the factorised expression for $x^3-27$?

1. $(x-3)(x^2+3x+9)$

2. $(x+3)(x^2+3x+9)$

3. $(x-3)(x^2-3x+9)$

4. $(x-3)(x^2+3x-9)$

Q. Factorise $4a^2+4ab+b^2$ .

1. $(a+2b{)}^2$
2. $(2a-b{)}^2$
3. $(4a+b{)}^2$
4. $(2a+b{)}^2$

Q.

Question 92 (i)

Factorise the following using the identity $a^2-b^2=(a+b)(a-b).$

$x^2-9$

Q. Factorise:

(i) (p² – 2pq + q²) – r²

(ii) (x + y)² – (x – y)²

[1 mark + 2 marks = 3 marks]

Q.

Question 92 (xviii)

Factorise the following using the identity $a^2-b^2=(a+b)(a-b).$

$a^4-(a-b{)}^4$

Q. The expression $x^9-x$ has:

1. 5 factors
2. 4 factors
3. 2 factors
4. 3 factors

Q.

Factorise $4{(x-y)}^2-9{(x-y)}^4$.

Q.

$36a^2-81canbefactorizedas$______.

1. $(6a+81)(6a-81)$

2. $(6a-9)(36a+9)$

3. $(6a+9)(6a-9)$
4. $(36a+9)(36a-9)$

Q. If $m=-2,$ then find the value of
$m^2+6m.$

1. 9
2. - 8
3. 8
4. - 9

Q.

One of the factors of $x^2-2x-15$ is _____.

1. x - 15

2. x+3

3. x-3

4. x+5

Q. One of the factors of $x^2+\frac{1}{x^2}+2-2x-\frac{2}{x}$ is:

1. $x-\frac{1}{x}$
2. $x^2+\frac{1}{x^2}$
3. $x+\frac{1}{x}$
4. $x-\frac{1}{x}-1$

Q.

Which of the following is a factor of $x^2-6x-16$?

1. x + 8

2. 8 - x

3. x - 6

4. x - 2

Q. Factors of $27x^3+y^3+z^3-9xyz$ are:

1. $(3x+y+z)(9x^2+y^2+z^2-3xy-yz-3xz)$
2. $(3x+y+z)(9x^2+y^2+z^2+3xy+yz+3xz)$
3. $(3x-y+z)(9x^2+y^2-z^2+3xy+yz+3xz)$
4. $(3x-y-z)(9x^2+y^2+z^2-3xy-yz-3xz)$

Q.

A factor of $a^2-2ab+b^2-c^2$ is ___________.

1. a-b+c

2. a-b-c

3. Both 1 and 2

4. a+b-c

Q. Question 90 (x)

Factorise the following, using the identity, $a^2-2ab+b^2=(a-b{)}^2$.

$\frac{x^2}{4}-2x+4$