Answer :

Sure! Let's factor the expression [tex]\(21x^2 + 70x^4\)[/tex] completely by breaking it down into simpler steps.

### Step 1: Identify the Greatest Common Factor (GCF)
First, look for the greatest common factor in the terms of the expression [tex]\(21x^2\)[/tex] and [tex]\(70x^4\)[/tex].

- Coefficients: The GCF of the coefficients [tex]\(21\)[/tex] and [tex]\(70\)[/tex] is [tex]\(7\)[/tex].
- Variable terms: Both terms have [tex]\(x^2\)[/tex], so the GCF for the variable part is [tex]\(x^2\)[/tex].

Thus, the GCF of the entire expression is [tex]\(7x^2\)[/tex].

### Step 2: Factor Out the GCF
Now, we can factor out [tex]\(7x^2\)[/tex] from each term in the expression:

[tex]\[
21x^2 + 70x^4 = 7x^2(3) + 7x^2(10x^2)
\][/tex]

This simplifies to:

[tex]\[
21x^2 + 70x^4 = 7x^2(3 + 10x^2)
\][/tex]

### Step 3: Write the Fully Factored Expression
After factoring out the GCF, the fully factored expression is:

[tex]\[
7x^2(10x^2 + 3)
\][/tex]

And that's the complete factorization of the original expression!

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