To expand the expression [tex]\( 4x^3(4a - 5x^4 + 2x^2) \)[/tex] step-by-step, follow these instructions:
1. Distribute [tex]\(4x^3\)[/tex] to each term inside the parentheses:
Let's break it down term by term.
2. First Term Inside the Parentheses: [tex]\(4a\)[/tex]
[tex]\[
4x^3 \cdot 4a = 16ax^3
\][/tex]
3. Second Term Inside the Parentheses: [tex]\(-5x^4\)[/tex]
[tex]\[
4x^3 \cdot (-5x^4) = -20x^7
\][/tex]
4. Third Term Inside the Parentheses: [tex]\(2x^2\)[/tex]
[tex]\[
4x^3 \cdot 2x^2 = 8x^5
\][/tex]
5. Combine All the Distributed Terms Together:
[tex]\[
16ax^3 - 20x^7 + 8x^5
\][/tex]
So, the expanded expression is:
[tex]\[
16ax^3 - 20x^7 + 8x^5
\][/tex]
