Factorisation of Algebraic Expressions Using Identities

Q.

Factorise: $x^2+10x+25$

1. (x + 5)(x - 5)

2. 

3. 

4. (x + 5)(x + 2)

Q.

Use a suitable identity to get each of the following products.

$\left(x+3\right)\left(x+3\right)$

Q. $16x^5-144x^3$ =

1. $16x^3(x-3)(x-3)$
2. $16x^5(1-9x^2)$
3. $16x^3(3+x)(3-x)$
4. $16x^3(x+3)(x-3)$

Q. $\text{If}X=1-a^2\text{and}Y=1-b^2,\text{then what is}{X}^2+Y^2?$

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

Q. $Factorise:16x^2-16x+4$

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

Q.

Write the like terms of the expression $m^2-mn+m^2{n}^2+4-2mn$.

Q.

Factorise: $x^2+12x+36$.

1. $(x+6)(x+2)$

2. $(x+6)(x+6)$

3. $(x+4)(x+3)$

4. $(x+3)(x+12)$

Q.

Factors of $49p^2-36$ are:

1. (7p - 6) (7p + 6)

2. (7p - 6) (7p - 6)

3. (7p + 6) (7p + 6)

4. (6p - 7) (7p - 6)

Q. Evaluate : $(2x-5y)(3x+7y)(8x-9y)$.

Q.

Factorise:$4y^2-9$

1. (7y− 5)²

2. (5y− 3)²

3. (2y− 5)²

4. (2y− 3)²

Q. Factorise $z^2-(x^2+2xy+y^2)$ using identities.

1. $(x+y-z)(z-x-y)$
2. $(x+y+z)(z+x-y)$
3. $(x+y+z)(z-x+y)$
4. $(x+y+z)(z-x-y)$

Q.

On factorising $25-49x^2$, we get

1. (5x+7)(5x+2)

2. (7x+5)(5x+3)

3. (7x+5)²

4. (3x+7)²

Q. $\text{Express}15a^{2}b{c}^3\text{as the product of its factors.}$

1. $3\times 5\times a^2\times b\times c^3$
2. $3\times 5\times a\times a\times b\times c\times c\times c$
3. $15\times a\times a\times b\times c\times c\times c$
4. $15\times a^2\times b\times c^3$

Q.

$25x^2-4$ can be factorised as:

1. (5a + 2) (5a + 2)

2. (5a - 2) (5a - 2)

3. (5a + 2) (5a - 2)
4. (5a + 12) (5a - 12)

Q. One of the factors of $(a^2-b^2)(c^2-d^2)-4abcd$ is ______.

1. $(ac-bd+bc+ad)$
2. $(ac+bd+bc+ad)$
3. $(ac+bd+bc-ad)$
4. $(ac-bd+bc-ad)$

Q. Factorisation of $z^2-(x^2+2xy+y^2)$ = .

1. $(x+y-z)(z-x-y)$
   
2. $(x+y+z)(z+x-y)$
   
3. $(x+y+z)(z-x+y)$
   
4. $(x+y+z)(z-x-y)$
   

Q. $(3x+2{)}^2-(3x-2{)}^2$ = .

1. $24x$
2. $-24x$
3. $2(9x^2+4$)
4. $2(9x^2-4$)

Q.

Write the coefficient of

$x^2$ in $-\frac{5}{3}{x}^{2}y$

Q.

How do you factor ${\mathrm{x}}^3+{\mathrm{y}}^3$?

Q. $\text{Factorise the expression:}5m^2+50m+125$

1. $(m-5{)}^2$
   
2. $5(m+5{)}^2$
3. $5(m-5)(m+5)$
4. $m^2-5^2$

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

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

Q.

Identify monomials, binomials, trinomials and polynomials from the following.

$4abc+2a$

Q. $16x^5-144x^3$ =

1. $16x^3(x-3)(x-3)$
2. $16x^5(1-9x^2)$
3. $16x^3(3+x)(3-x)$
4. $16x^3(x+3)(x-3)$

Q. Factorising $x^2+16x+63$ we get, $(x+7)$ and .

1. $(x-7)(x+9)$
2. $(x+7)(x-9)$
3. $(x+9)$
4. $(x-9)$

Q. Choose the correct pair.

1. $a^2+4a+4$
2. $a^2-2a+1$
3. $2(a^2+1)$
4. $(a^2-9)$
5. $(a+1{)}^2+(a-1{)}^2$
6. $(a+3)(a-3)$
7. $(a-1{)}^2$
8. $(a+2{)}^2$

Q.

State whether each pair of the terms given below is like or unlike.

$\frac{2}{5}x,-3x$