Factoring by Common Factors & by Grouping

In lesson, we will look at factoring by common factors and factoring of polynomials by grouping.

Factoring By Common Factors

The first step in factorising is to find and extract the GCF of all the terms.

Example:

Factorise the following algebraic expressions:

a) xyz – x²z

b) 6a²b + 4bc

Solution:

The following video shows an example of simple factoring or factoring by common factors.

Factoring By Grouping

When an expression has an even number of terms and there are no common factors for all the terms, we may group the terms into pairs and find the common factor for each pair:

Example:

Factorise the following expressions:

a) ax + ay + bx + by

b) 2x + 8y – 3px –12py

c) 3x – 3y + 4ay – 4ax

Solution:

a) ax + ay + bx + by
= a(x + y) + b(x + y)
= (a + b)(x + y)

b) 2x + 8y – 3px –12py
= 2(x + 4y) –3p(x + 4y)
= (2 – 3p)(x + 4y)

c) 3x – 3y + 4ay – 4ax
= 3(x – y) + 4a(y – x)
= 3(x – y) – 4a(x – y)
= (3 – 4a)( x – y)

The following video gives another example of factoring by grouping.

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