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].
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].
