ac+ad+bc+bd type expressions

2.  ac+ad+bc+bd type expressions

In such types of algebraic sentences one factor is common with two terms and another factor is common with other two similar terms i-e ‘a’ is common with first two terms and ‘b’ is common with last two similar terms. When these common factors are separated we get two algebraic expressions factoring.

i-e

ac+ad+bc+bd= a(c+d)+b(c+d)

If we put this in two bracket, we get;

\Rightarrow ac+ad+bc+bd= [a(c+d)+b(c+d)]

Now within brackets'[]’ we see that (c+d) is common. Take this out and we get;

\Rightarrow ac+ad+bc+bd= (c+d)[a+b]

So, given expression has been splited into two algebraic factors (c+d) and (a+b). if we multiply these two factors together , the product will be the original given expression.

Example: Factorize 3x-3a+xy-ay

Solution:

Here we notice that ‘3’ is common with first two terms and ‘y’ is common with last two terms,

3x-3a+xy-ay = 3(x-a)+y(x-a)

putting brackets;

3x-3a+xy-ay = [3(x-a)+y(x-a)]

Now within brackets ‘[]’ (x-a) is common which we take out;

 \Rightarrow 3x-3a+xy-ay = (x-a)[3+y]

So we done factorization getting (x-a) and (3+y) two factors. If we multiply these two together we will get the original given expression.

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