Answer :
Sure! Let's multiply the expression [tex]\(5x^2(2x^2 + 13x - 5)\)[/tex] step by step using the distributive property. Here's how you can do it:
1. Distribute [tex]\(5x^2\)[/tex] across each term inside the parentheses:
[tex]\[
5x^2 \cdot 2x^2 = (5 \cdot 2)x^{2+2} = 10x^4
\][/tex]
2. Multiply [tex]\(5x^2\)[/tex] with the second term [tex]\(13x\)[/tex]:
[tex]\[
5x^2 \cdot 13x = (5 \cdot 13)x^{2+1} = 65x^3
\][/tex]
3. Multiply [tex]\(5x^2\)[/tex] with the third term [tex]\(-5\)[/tex]:
[tex]\[
5x^2 \cdot (-5) = (5 \cdot -5)x^2 = -25x^2
\][/tex]
Putting it all together, the expanded expression is:
[tex]\[
10x^4 + 65x^3 - 25x^2
\][/tex]
This matches one of the given options, which is [tex]\(10x^4 + 65x^3 - 25x^2\)[/tex]. So, the correct answer is the first choice.
1. Distribute [tex]\(5x^2\)[/tex] across each term inside the parentheses:
[tex]\[
5x^2 \cdot 2x^2 = (5 \cdot 2)x^{2+2} = 10x^4
\][/tex]
2. Multiply [tex]\(5x^2\)[/tex] with the second term [tex]\(13x\)[/tex]:
[tex]\[
5x^2 \cdot 13x = (5 \cdot 13)x^{2+1} = 65x^3
\][/tex]
3. Multiply [tex]\(5x^2\)[/tex] with the third term [tex]\(-5\)[/tex]:
[tex]\[
5x^2 \cdot (-5) = (5 \cdot -5)x^2 = -25x^2
\][/tex]
Putting it all together, the expanded expression is:
[tex]\[
10x^4 + 65x^3 - 25x^2
\][/tex]
This matches one of the given options, which is [tex]\(10x^4 + 65x^3 - 25x^2\)[/tex]. So, the correct answer is the first choice.
