Answer :
To solve [tex]\((4x^2 + 7x)(5x^2 - 3x)\)[/tex], let's expand this expression step by step using the distributive property (also known as the FOIL method, which is usually applied to binomials).
1. Multiply the first terms in each binomial:
[tex]\[
4x^2 \cdot 5x^2 = 20x^4
\][/tex]
2. Multiply the outer terms in each binomial:
[tex]\[
4x^2 \cdot (-3x) = -12x^3
\][/tex]
3. Multiply the inner terms in each binomial:
[tex]\[
7x \cdot 5x^2 = 35x^3
\][/tex]
4. Multiply the last terms in each binomial:
[tex]\[
7x \cdot (-3x) = -21x^2
\][/tex]
Now that we have all the products, let's combine them:
- Combine the [tex]\(x^3\)[/tex] terms:
[tex]\[
-12x^3 + 35x^3 = 23x^3
\][/tex]
Putting everything together, we get the final expression:
[tex]\[
20x^4 + 23x^3 - 21x^2
\][/tex]
So, the correct answer is D: [tex]\(20x^4 + 23x^3 - 21x^2\)[/tex].
1. Multiply the first terms in each binomial:
[tex]\[
4x^2 \cdot 5x^2 = 20x^4
\][/tex]
2. Multiply the outer terms in each binomial:
[tex]\[
4x^2 \cdot (-3x) = -12x^3
\][/tex]
3. Multiply the inner terms in each binomial:
[tex]\[
7x \cdot 5x^2 = 35x^3
\][/tex]
4. Multiply the last terms in each binomial:
[tex]\[
7x \cdot (-3x) = -21x^2
\][/tex]
Now that we have all the products, let's combine them:
- Combine the [tex]\(x^3\)[/tex] terms:
[tex]\[
-12x^3 + 35x^3 = 23x^3
\][/tex]
Putting everything together, we get the final expression:
[tex]\[
20x^4 + 23x^3 - 21x^2
\][/tex]
So, the correct answer is D: [tex]\(20x^4 + 23x^3 - 21x^2\)[/tex].
