In factorization when monomial is common factor we know, that an algebraic expression is the sum or the difference of monomials.

In order to factorize follow the following steps:

**Step 1:** Write the algebraic expression.

**Step 2:** Find the HCF of all the terms of the given algebraic expression.**Step 3:** Express each terms of the algebraic expression as the product of H.C.F and the quotient when it is divided by the H.C.F.

i.e. divide each term of the given expression by the HCF.**Step 4:** Now use distributive property of multiplication over addition or subtraction to express the algebraic expression as the product of H.C.F and the quotient of the expression divided by the H.C.F.

i.e. write the given expression as the product of this HCF and the quotient obtained in step 2.

**Step 5:** Keep the H.C.F. outside the bracket and the quotients obtained within the bracket.

Solved examples of factorization when monomial
is common:

**1. Factorize
each of the following: **

(i) 5x + 20**Solution: **

5x + 20

= 5(x + 4)

2n

= n(2n + 3)

(iii) 3x

3x

= 3xy(x - 2y)

(iv) 6ab - 9bc

**Solution: **

6ab - 9bc

= 3b(2a - 3c)

The H.C.F. of 6a

The H.C.F. of 6 and 27 = 3

The H.C.F. of a

Therefore, the H.C.F. of 6a

Now, 6a

= 3abc(2ab + 9)

Therefore, the factor of 6a

18a

18a

HCF of 18a

Therefore, 18a

**8th Grade Math Practice**

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