To factor the expression [tex]\( 72x^2 + 36xy - 27x \)[/tex], follow these steps:
1. Identify the common factors:
First, we need to find the greatest common divisor (GCD) of the coefficients (72, 36, and 27). The GCD of 72, 36, and 27 is 9.
2. Factor out the GCD:
Since 9 is a common factor of all the terms in the expression, we can factor out 9 from each term. Additionally, we notice that [tex]\(x\)[/tex] is also a common factor in all the terms. So, we will factor out [tex]\(9x\)[/tex].
3. Rewrite each term after factoring out [tex]\(9x\)[/tex]:
- From [tex]\(72x^2\)[/tex]: When we factor out [tex]\(9x\)[/tex], we are left with [tex]\(\frac{72x^2}{9x} = 8x\)[/tex].
- From [tex]\(36xy\)[/tex]: When we factor out [tex]\(9x\)[/tex], we are left with [tex]\(\frac{36xy}{9x} = 4y\)[/tex].
- From [tex]\(-27x\)[/tex]: When we factor out [tex]\(9x\)[/tex], we are left with [tex]\(\frac{-27x}{9x} = -3\)[/tex].
4. Combine the factored terms:
When we put these factored terms together, the expression becomes:
[tex]\[
9x (8x + 4y - 3)
\][/tex]
Thus, the factored form of [tex]\(72x^2 + 36xy - 27x\)[/tex] is:
[tex]\[
9x (8x + 4y - 3)
\][/tex]
