Answer :
To solve the expression [tex]\(\left(4x^2 + 7x\right) \left(5x^2 - 3x\right)\)[/tex], follow these steps:
1. Distribute each term in the first polynomial to both terms in the second polynomial. We'll break it down step-by-step:
[tex]\[
(4x^2 + 7x) \cdot (5x^2 - 3x)
\][/tex]
2. Distribute [tex]\(4x^2\)[/tex] to each term in the second polynomial:
[tex]\[
4x^2 \cdot 5x^2 = 20x^4
\][/tex]
[tex]\[
4x^2 \cdot (-3x) = -12x^3
\][/tex]
3. Distribute [tex]\(7x\)[/tex] to each term in the second polynomial:
[tex]\[
7x \cdot 5x^2 = 35x^3
\][/tex]
[tex]\[
7x \cdot (-3x) = -21x^2
\][/tex]
4. Combine all these terms together:
[tex]\[
20x^4 - 12x^3 + 35x^3 - 21x^2
\][/tex]
5. Combine like terms (combine the [tex]\(x^3\)[/tex] terms):
[tex]\[
20x^4 + (35x^3 - 12x^3) - 21x^2
\][/tex]
[tex]\[
20x^4 + 23x^3 - 21x^2
\][/tex]
Therefore, the expanded form of [tex]\(\left(4x^2 + 7x\right) \left(5x^2 - 3x\right)\)[/tex] is:
[tex]\[
20x^4 + 23x^3 - 21x^2
\][/tex]
Matching this with the given choices, the correct answer is:
D. [tex]\(20x^4 + 23x^3 - 21x^2\)[/tex]
1. Distribute each term in the first polynomial to both terms in the second polynomial. We'll break it down step-by-step:
[tex]\[
(4x^2 + 7x) \cdot (5x^2 - 3x)
\][/tex]
2. Distribute [tex]\(4x^2\)[/tex] to each term in the second polynomial:
[tex]\[
4x^2 \cdot 5x^2 = 20x^4
\][/tex]
[tex]\[
4x^2 \cdot (-3x) = -12x^3
\][/tex]
3. Distribute [tex]\(7x\)[/tex] to each term in the second polynomial:
[tex]\[
7x \cdot 5x^2 = 35x^3
\][/tex]
[tex]\[
7x \cdot (-3x) = -21x^2
\][/tex]
4. Combine all these terms together:
[tex]\[
20x^4 - 12x^3 + 35x^3 - 21x^2
\][/tex]
5. Combine like terms (combine the [tex]\(x^3\)[/tex] terms):
[tex]\[
20x^4 + (35x^3 - 12x^3) - 21x^2
\][/tex]
[tex]\[
20x^4 + 23x^3 - 21x^2
\][/tex]
Therefore, the expanded form of [tex]\(\left(4x^2 + 7x\right) \left(5x^2 - 3x\right)\)[/tex] is:
[tex]\[
20x^4 + 23x^3 - 21x^2
\][/tex]
Matching this with the given choices, the correct answer is:
D. [tex]\(20x^4 + 23x^3 - 21x^2\)[/tex]
