High School

Dear beloved readers, welcome to our website! We hope your visit here brings you valuable insights and meaningful inspiration. Thank you for taking the time to stop by and explore the content we've prepared for you.
------------------------------------------------ Factor the expression:

[tex] 18x^4 + 27x^2 [/tex]

Answer :

Sure! Let's factor the expression [tex]\(18x^4 + 27x^2\)[/tex] step by step.

1. Identify the Greatest Common Factor (GCF):

First, we notice that each term in the expression has a common factor. Both terms, [tex]\(18x^4\)[/tex] and [tex]\(27x^2\)[/tex], can be divided by [tex]\(9x^2\)[/tex].

2. Factor Out the GCF:

- The GCF of the numerical coefficients 18 and 27 is 9.
- The variable terms [tex]\(x^4\)[/tex] and [tex]\(x^2\)[/tex] have a common factor of [tex]\(x^2\)[/tex].

So, the GCF of the entire expression is [tex]\(9x^2\)[/tex].

Factoring out [tex]\(9x^2\)[/tex] from the expression gives:

[tex]\[
18x^4 + 27x^2 = 9x^2(2x^2 + 3)
\][/tex]

3. Check Your Work:

You can verify this factorization by distributing [tex]\(9x^2\)[/tex] back:

[tex]\[
9x^2(2x^2) + 9x^2(3) = 18x^4 + 27x^2
\][/tex]

This confirms that our factorization is correct.

In conclusion, the factored form of the expression [tex]\(18x^4 + 27x^2\)[/tex] is [tex]\(9x^2(2x^2 + 3)\)[/tex].