Factorization of Expressions of the Form x^2 + (a + b)x + ab | How to Factorize Algebraic Expressions using Identity x^2 + (a + b)x + ab?

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There are several Identities and using them makes the factorization process much simple and easy. In this article, you will know how to factorize the expressions of the form x2 + (a + b)x + ab or can be put in the form. Get to know how to do the factorization algebraic expressions of the form x2 + (a + b)x + ab with the suitable examples provided and learn the concept in depth.

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How to Factorize Algebraic Expression in the Form of Identity x2 + (a + b)x + ab?

Follow the simple steps listed below to learn factorization of algebraic expressions in the form or can be put in the form of x2 + (a + b)x + ab explained step by step. They are as follows

  • Take the constant term (with the sign) q.
  • Now split q into two factors, say a, b with suitable signs, and the sum should equal to the coefficient of x, i.e., a + b = p
  • Pair one of these i.e. ax with x2 and the other bx with the constant term q and then factorize.

Remember if you are unable to factorize conveniently then the factorization of x2 + px + q can’t be factorized as above.

Solved Examples on Factorization of Expressions of the form x2 + (a + b)x + ab

Example 1.
Factorize the expression z2 + 6z + 9?
Solution:
Given Expression = z2 + 6z + 9
We can rewrite and put the expression in the form of identity x2 + (a + b)x + ab as under whose constant terms make up product 9 and sum a+b=6
= z2 + 3z+3z + 3.3
= z(z+3)+3(z+3)
=(z+3)(z+3)

Example 2.
Factorize m2 – 6m + 8?
Solution:
Given Expression =m2 – 6m + 5
We can rewrite and put the expression in the form of identity x2 + (a + b)x + ab as under whose constant terms make up product 8 and sum a+b=-6
= m2 – 2m-4m + 8
= m(m-2)-4(m-2)
= (m-2)(m-4)

Example 3.
Factorize b2 + 7b + 12?
Solution:
Given Expression = b2 + 7b + 12
We can rewrite and put the expression in the form of identity x2 + (a + b)x + ab as under whose constant terms make up product 12 and sum a+b=7
= b2 + 7b + 12
= b2+4b+3b+12
= b(b+4)+3(b+4)
= (b+3)(b+4)

Example 4.
Factorize x2 + 10x + 25?
Solution:
Given Expression = x2 + 10x + 25
We can rewrite and put the expression in the form of identity x2 + (a + b)x + ab as under whose constant terms make up product 25 and sum a+b=10
= x2 + 10x + 25
= x2+5x+5x+25
= x(x+5)+5(x+5)
= (x+5)(x+5)

Example 5.
Factorize the expression x2 – 20x + 100?
Solution:
Given expression = x2 – 20x + 100
We can rewrite and put the expression in the form of identity x2 + (a + b)x + ab as under whose constant terms make up product 25 and sum a+b=10
= x2 – 20x + 100
= x2 -10x-10x + 100
= x(x-10)-10(x-10)
=(x-10)(x-10)

Example 6.
Factorize m2 + 8m + 16?
Solution:
Given Expression m2 + 8m + 16
We can rewrite and put the expression in the form of identity x2 + (a + b)x + ab as under whose constant terms make up product 16 and sum a+b=8
= m2 + 8m + 16
= m2 + 4m+4m + 16
=m(m+4)+4(m+4)
=(m+4)(m+4)

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