Factorising Expressions of the Form (x+a)(x+b)

Q.

Factorise the expression and divide them as directed: $5pq\left(p^2-q^2\right)÷2p\left(p+q\right)$.

Q. $\text{If}{x}^2-4x-12=(x+m)(x+n)$,
then find the value of $(m+n).$

1. $2$
2. $-2$
3. $4$
4. $-4$

Q.

Question 92 (v)

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

$28a{y}^2-175a{x}^2$

Q. Question 2(v)
Factorise
$(l+m{)}^2-(l-m{)}^2$

Q. Question 89 (iii)

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

$x^2+14x+49$

Q. Factorise:
$2m^2+20m+50.$

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

Q. Question 89 (xiii)

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

$2x^3+24x^2+72x$

Q.

Question 92 (ix)

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

$\frac{2p^2}{25}-32q^2$

Q.

Find and correct the errors (if any) in the following expressions:

$i.\left)\right(5x-2{)}^2=25x^2+4-20x$

$ii.\left)\right(3x+2{)}^2=3x^2+6x+4$

Q.

Question 92 (vii)

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

$25a{x}^2-25a$

Q. Factorise the expression:
$x^2+5x-6$

1. $(x+6)(x-1)$
2. $(x+6)(x+1)$
3. $(x+3)(x-2)$
4. $(x+3)(x+2)$

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.

Question 92 (xiv)

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

$\frac{4x^2}{9}-\frac{9y^2}{16}$

Q. $\text{Factorise the expression}48+8m-m^2.$

1. $(4+m)(12-m)$
2. $(4-m)(12-m)$
3. $(4+m)(12+m)$
4. $(6+m)(8-m)$

Q.

Factorize the following expression:

$125-8x^3-27y^3-90xy$

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

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

Q. $\text{If}{x}^2-4x-12=(x+m)(x+n)$,
then find the value of $(m+n).$

1. $2$
2. $-2$
3. $4$
4. $-4$

Q. $\text{Factorise:}(2l+m{)}^2-8lm$

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.

Question 92 (xxx)

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

$x^2-\frac{y^2}{100}$

Q. $\text{Factorise:}(2l+m{)}^2-8lm$

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

Q.

Which of the following is/are the irreducible factor(s) of $3m^2+9m+6?$

1. 3

2. $m+2$

3. $m+3$

4. $m+1$