Factorizing Algebraic Expressions can be a difficult task for certain students who aren’t strong in the fundamentals of maths. Such students will find this article quite a handy resource as it explains different problems on the factorization of expressions of the form x^{2} +(a + b)x +ab.

Go through the entire article and learn how to factorize algebraic expressions using the identity x^{2} +(a + b)x +ab and arrive at the result easily. Practice the example questions on the factorization of expressions of the form x^{2} +(a + b)x +ab regularly and attempt the exam with utmost confidence and score well.

See More:

- Factorization of Expressions of the Form x
^{2}+ (a + b)x + ab - Factorization of Expressions of the Form ax
^{2}+ bx + c, a ≠ 1

## Examples on Factorization of Algebraic Expressions using Identity x^{2} +(a + b)x +ab

**Example 1.
**Factorize x

^{2}+ 6x + 8?

**Solution:**

Given Expression = x

^{2}+ 6x + 8

Here constant term = 8= 4*2=8 Coefficient of x = 6 i.e.(4+2)

= x

^{2}+ 4x +2x+ 8

= x(x+4)+2(x+4)

=(x+4)(x+2)

**Example 2.
**Factorize x

^{2}+ 21x + 108?

**Solution:**

Given Expression = x

^{2}+ 21x + 108

Here constant term = 108= 12*9=108 Coefficient of x = 21 i.e.(12+9)

=x

^{2}+ 12x +9x+ 108

=x(x+12)+9(x+12)

=(x+9)(x+12)

**Example 3.
**Factorize x

^{2}y

^{2}– 2xy – 63?

**Solution:**

Given Expression = x

^{2}y

^{2}– 2xy – 63

here Constant Term = -63=7*-9 =-63, Coefficient of xy=-2=-9+7

= x

^{2}y

^{2}– 9xy+7xy – 63

=xy(xy-9)+7(xy-9)

=(xy-9)(xy+7)

**Example 4.
**Factorize 6x

^{2}+5x +6?

**Solution:**

Given Expression = 6x

^{2}+5 x +6

Here Constant Term = 6*6 =36 =9*4, Coefficient of x= 5=9-4

=6x

^{2}+9x-4x +6

=3x(2x+3)-2(2x-3)

=(3x-2)(2x+3)

**Example 5.
**Factorize 5x

^{2}+25x+25?

**Solution:**

Given Expression = 5x

^{2}+25x+25

Here Constant Term = 5*25=125, Coefficient of x =25=20+5

= 5x

^{2}+20x+5x+25

= 5x(x+5)+5(x+5)

= (5x+5)(x+5)

**Example 6.
**Factorize 2x

^{2}-5x-3?

**Solution:**

Given Expression = 2x

^{2}-5x -3

Here Constant Term = 2*-3 =-6, Coefficient of x= -5=-6+1

=2x

^{2}-5x-3

=2x

^{2}-6x+x-3

=2x(x-3)+1(x-3)

=(2x+1)(x-3)

**Example 7.
**Factorize 3x

^{2}+13x+4?

**Solution:**

Given Expression = 3x

^{2}+13x+4

Here Constant Term =3*4 =12, Coefficient of x= 13=12+1

=3x

^{2}+13x+4

=3x

^{2}+12x+x+4

=3x(x+4)+1(x+4)

=(3x+1)(x+4)

**Example 8.
**Factorize r

^{2}-10r + 21?

**Solution:**

Given Expression = r

^{2}-10r + 21

Here Constant Term =1*21 =21, Coefficient of a=-10=-7-3

=r

^{2}-10r + 21

=r

^{2}-7r-3r + 21

=r(r-7)-3(r-7)

=(r-7)(r-3)