Alright class, let's factorise the expression [tex]\(8x + 12\)[/tex] step by step.
1. Identify the common factor:
Look at the constants and coefficients in both terms. We have [tex]\(8x\)[/tex] and [tex]\(12\)[/tex]. The greatest common factor (GCF) of 8 and 12 is 4.
2. Factor out the GCF:
We factor out 4 from each term in the expression. This means rewriting each term as a product of 4 and another term:
[tex]\[
8x + 12 = 4 \cdot 2x + 4 \cdot 3
\][/tex]
3. Rewrite the expression:
Now, we can use the distributive property in reverse, which is factoring out the common factor:
[tex]\[
4(2x + 3)
\][/tex]
So, the factorised form of [tex]\(8x + 12\)[/tex] is:
[tex]\[
4(2x + 3)
\][/tex]
And that is the final answer.
