College

Simplify the expression:

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

A. [tex]20x^4 + 35x^3 - 21x^2[/tex]

B. [tex]20x^4 + 35x^2 - 21x[/tex]

C. [tex]20x^4 + 23x^2 - 21x[/tex]

D. [tex]20x^4 + 23x^3 - 21x^2[/tex]

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]