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Multiply:

\[
\left(4x^2 + 7x\right)\left(5x^2 - 3x\right)
\]

A. \[ 20x^4 + 35x^2 - 21x \]
B. \[ 20x^4 + 23x^3 - 21x^2 \]
C. \[ 20x^4 + 35x^3 - 21x^2 \]
D. \[ 20x^4 + 23x^2 - 21x \]

Answer :

Let's multiply the expressions [tex]\((4x^2 + 7x)\)[/tex] and [tex]\((5x^2 - 3x)\)[/tex] step-by-step:

1. Distribute [tex]\(4x^2\)[/tex] over [tex]\((5x^2 - 3x)\)[/tex]:

- Multiply [tex]\(4x^2\)[/tex] by [tex]\(5x^2\)[/tex]:
[tex]\[
4x^2 \times 5x^2 = 20x^4
\][/tex]

- Multiply [tex]\(4x^2\)[/tex] by [tex]\(-3x\)[/tex]:
[tex]\[
4x^2 \times (-3x) = -12x^3
\][/tex]

2. Distribute [tex]\(7x\)[/tex] over [tex]\((5x^2 - 3x)\)[/tex]:

- Multiply [tex]\(7x\)[/tex] by [tex]\(5x^2\)[/tex]:
[tex]\[
7x \times 5x^2 = 35x^3
\][/tex]

- Multiply [tex]\(7x\)[/tex] by [tex]\(-3x\)[/tex]:
[tex]\[
7x \times (-3x) = -21x^2
\][/tex]

3. Combine all terms:

Arrange all the products and then combine the like terms:
[tex]\[
20x^4 + (-12x^3) + 35x^3 + (-21x^2)
\][/tex]

- Combine the [tex]\(x^3\)[/tex] terms:
[tex]\[
-12x^3 + 35x^3 = 23x^3
\][/tex]

Thus, the resulting expression is:
[tex]\[
20x^4 + 23x^3 - 21x^2
\][/tex]

The correct answer is [tex]\(20x^4 + 23x^3 - 21x^2\)[/tex], which matches option B.

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