Answer :
To factor the expression [tex]\(70x^4 + 80x^2\)[/tex] completely, we can follow these steps:
1. Identify the Greatest Common Factor (GCF):
The terms in the expression are [tex]\(70x^4\)[/tex] and [tex]\(80x^2\)[/tex]. First, find the GCF of the coefficients 70 and 80. The GCF is 10.
Both terms also share a common factor involving [tex]\(x\)[/tex], specifically [tex]\(x^2\)[/tex]. Therefore, the GCF of the entire expression is [tex]\(10x^2\)[/tex].
2. Factor out the GCF:
Divide each term in the expression by the GCF and factor it out:
[tex]\[
70x^4 + 80x^2 = 10x^2(7x^2) + 10x^2(8)
\][/tex]
So, when factored by the GCF, the expression becomes:
[tex]\[
10x^2(7x^2 + 8)
\][/tex]
3. Check for further factorization:
Now, look at the expression inside the parentheses, [tex]\(7x^2 + 8\)[/tex]. Check if it can be factored further. Since it doesn't have any common factors and is not a difference of squares or another easily factorable form, it remains as is.
Therefore, the completely factored form of the expression is:
[tex]\[
10x^2(7x^2 + 8)
\][/tex]
1. Identify the Greatest Common Factor (GCF):
The terms in the expression are [tex]\(70x^4\)[/tex] and [tex]\(80x^2\)[/tex]. First, find the GCF of the coefficients 70 and 80. The GCF is 10.
Both terms also share a common factor involving [tex]\(x\)[/tex], specifically [tex]\(x^2\)[/tex]. Therefore, the GCF of the entire expression is [tex]\(10x^2\)[/tex].
2. Factor out the GCF:
Divide each term in the expression by the GCF and factor it out:
[tex]\[
70x^4 + 80x^2 = 10x^2(7x^2) + 10x^2(8)
\][/tex]
So, when factored by the GCF, the expression becomes:
[tex]\[
10x^2(7x^2 + 8)
\][/tex]
3. Check for further factorization:
Now, look at the expression inside the parentheses, [tex]\(7x^2 + 8\)[/tex]. Check if it can be factored further. Since it doesn't have any common factors and is not a difference of squares or another easily factorable form, it remains as is.
Therefore, the completely factored form of the expression is:
[tex]\[
10x^2(7x^2 + 8)
\][/tex]
