Problems on Factorization of Expressions of the Form x^2 +(a + b)x +ab | Factorization Questions in the Form of x^2 +(a + b)x +ab

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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 x2 +(a + b)x +ab.

Go through the entire article and learn how to factorize algebraic expressions using the identity x2 +(a + b)x +ab and arrive at the result easily. Practice the example questions on the factorization of expressions of the form x2 +(a + b)x +ab regularly and attempt the exam with utmost confidence and score well.

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Examples on Factorization of Algebraic Expressions using Identity x2 +(a + b)x +ab

Example 1.
Factorize x2 + 6x + 8?
Solution:
Given Expression = x2 + 6x + 8
Here constant term = 8= 4*2=8 Coefficient of x = 6 i.e.(4+2)
= x2 + 4x +2x+ 8
= x(x+4)+2(x+4)
=(x+4)(x+2)

Example 2.
Factorize x2 + 21x + 108?
Solution:
Given Expression = x2 + 21x + 108
Here constant term = 108= 12*9=108 Coefficient of x = 21 i.e.(12+9)
=x2 + 12x +9x+ 108
=x(x+12)+9(x+12)
=(x+9)(x+12)

Example 3.
Factorize x2y2 – 2xy – 63?
Solution:
Given Expression = x2y2 – 2xy – 63
here Constant Term = -63=7*-9 =-63, Coefficient of xy=-2=-9+7
= x2y2 – 9xy+7xy – 63
=xy(xy-9)+7(xy-9)
=(xy-9)(xy+7)

Example 4.
Factorize 6x2 +5x +6?
Solution:
Given Expression = 6x2 +5 x +6
Here Constant Term = 6*6 =36 =9*4, Coefficient of x= 5=9-4
=6x2 +9x-4x +6
=3x(2x+3)-2(2x-3)
=(3x-2)(2x+3)

Example 5.
Factorize 5x2+25x+25?
Solution:
Given Expression = 5x2+25x+25
Here Constant Term = 5*25=125, Coefficient of x =25=20+5
= 5x2+20x+5x+25
= 5x(x+5)+5(x+5)
= (5x+5)(x+5)

Example 6.
Factorize 2x2-5x-3?
Solution:
Given Expression = 2x2 -5x -3
Here Constant Term = 2*-3 =-6, Coefficient of x= -5=-6+1
=2x2-5x-3
=2x2-6x+x-3
=2x(x-3)+1(x-3)
=(2x+1)(x-3)

Example 7.
Factorize 3x2+13x+4?
Solution:
Given Expression = 3x2+13x+4
Here Constant Term =3*4 =12, Coefficient of x= 13=12+1
=3x2+13x+4
=3x2+12x+x+4
=3x(x+4)+1(x+4)
=(3x+1)(x+4)

Example 8.
Factorize r2 -10r + 21?
Solution:
Given Expression = r2 -10r + 21
Here Constant Term =1*21 =21, Coefficient of a=-10=-7-3
=r2 -10r + 21
=r2 -7r-3r + 21
=r(r-7)-3(r-7)
=(r-7)(r-3)

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