Answer :

To factor the expression [tex]\(3x^2 - 27\)[/tex], you can follow these steps:

1. Identify and Factor Out the Greatest Common Factor (GCF):

Look at the terms of the expression [tex]\(3x^2 - 27\)[/tex]. Both terms, [tex]\(3x^2\)[/tex] and [tex]\(27\)[/tex], have a common factor of 3.

[tex]\[
3x^2 - 27 = 3(x^2 - 9)
\][/tex]

2. Recognize the Difference of Squares:

The expression inside the parentheses, [tex]\(x^2 - 9\)[/tex], is a difference of squares. The difference of squares formula is:

[tex]\[
a^2 - b^2 = (a - b)(a + b)
\][/tex]

Here, [tex]\(a = x\)[/tex] and [tex]\(b = 3\)[/tex], because [tex]\(x^2\)[/tex] is [tex]\(x^2\)[/tex] and [tex]\(9\)[/tex] is [tex]\(3^2\)[/tex].

3. Apply the Difference of Squares Formula:

Replace [tex]\(x^2 - 9\)[/tex] with its factored form:

[tex]\[
x^2 - 9 = (x - 3)(x + 3)
\][/tex]

4. Combine the Factored Expressions:

Now substitute the factored form back into the expression:

[tex]\[
3(x^2 - 9) = 3(x - 3)(x + 3)
\][/tex]

So, the expression [tex]\(3x^2 - 27\)[/tex] factors to [tex]\(3(x - 3)(x + 3)\)[/tex].

Other Questions