Factorization by Using Quadratic Identities

Q. Which of the following are the factors of the expression $ax-ay+by-bx$ ?

1. $\left(a-b\right)$ and $\left(x+y\right)$
2. $\left(a-x\right)$ and $\left(b-y\right)$
3. $\left(a-b\right)$ and $\left(x-y\right)$
4. $\left(a-y\right)$ and $\left(b+x\right)$

Q. $a^8-2a^4{b}^4+b^8=$

1. (a2-b2)2
2. (a4-b4)2
3. (a4+b4)2

Q. The common factor method of factorization for a polynomial is based on ___ property.

Q. Which of the following is a factor of the given expression?

1. 6p - 9q
2. 7p - 9q
3. 6p + 9q
4. 7p + 9q

Q. The factors of (2x-3y)²+2(2x+3y)(X+y)+(X+y)² is (1)(2x-3y) and (3x-2y) (2)(2x+3y) and (3x+2y) (3)(3x+2y) and (3x-2y) (4) (3x-2y) and (3x-2y)

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

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

Q. Which of the following represents the factorisation of
$63x^2-175y^2?$

1. $7(x+5y)(x-5y)$
2. $7(3x+5y)(x-5y)$
3. $7(x+5y)(3x-5y)$
4. $7(3x+5y)(3x-5y)$

Q. $\text{Factorise:}{x}^4-(x-4{)}^4$

1. $16[x-2][x^2-4x+8]$
2. $16[x+2][x^2-4x+8]$
3. $16[x-2][x^2+4x+8]$
4. $32[x-2][x^2-4x+8]$

Q. Which of the following are the factors of the expression $ax-ay+by-bx$ ?

1. $\left(a-b\right)$ and $\left(x+y\right)$
2. $\left(a-x\right)$ and $\left(b-y\right)$
3. $\left(a-b\right)$ and $\left(x-y\right)$
4. $\left(a-y\right)$ and $\left(b+x\right)$

Q. Which of the following is a factor of '4a + 2b'?

1. 4a
2. 2b
3. 4
4. 2

Q. A factor of the expression 49- 25(a + b)(a + b) is:

1. 7+5a-5b
2. 7-5a+5b
3. 5-7a-7b
4. 7-5a-5b

Q. $x^2+18x+77$ = .

1. $(x-7)(x-11)$
2. $(x-7)(x+11)$
3. $(x+7)(x-11)$
4. $(x+7)(x+11)$

Q.

Factorise $x^2{y}^2-p^2{q}^2$.

Q. Which of the following represents the factorisation of the expression
$a^4+2a^2{b}^2+b^4?$

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

Q. $x^2+5x+6=$

1. $(x+3)(x+5)$
2. $(x+5{)}^2$
3. $(x+3)(x+2)$

Q.

Which of the following is/are factor(s) of
$49p^2-36?$

1. $(7p-6)$
2. $(7p+6)$
3. $(5p+6)$
4. $(6p+7)$

Q. Which of the following identities can be used to factorise $x^2+12x+36$?

1. $(x-a{)}^2$
2. $(x+a{)}^2$
3. $(x^2-a^2)$
4. None of the above.

Q.

$\text{Factorise:}25+70x+49x^2$

1. $(7x+5)(5x+3)$

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

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

4. $(3x+7{)}^2$

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. $(a+2{)}^2$