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Simplify [tex](4x^2 + 7x)(5x^2 - 3x)[/tex] and choose the correct option.

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

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

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

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

Answer :

Sure! Let's solve the expression [tex]\((4x^2 + 7x)(5x^2 - 3x)\)[/tex] step-by-step by using the distributive property (also known as the FOIL method when dealing with binomials).

1. Distribute [tex]\(4x^2\)[/tex] across the second binomial:

[tex]\[
4x^2 \cdot 5x^2 = 20x^4
\][/tex]

[tex]\[
4x^2 \cdot (-3x) = -12x^3
\][/tex]

2. Distribute [tex]\(7x\)[/tex] across the second binomial:

[tex]\[
7x \cdot 5x^2 = 35x^3
\][/tex]

[tex]\[
7x \cdot (-3x) = -21x^2
\][/tex]

3. Combine all the products:

[tex]\[
20x^4 + (-12x^3) + 35x^3 + (-21x^2)
\][/tex]

4. Combine the like terms:

[tex]\[
20x^4 + (35x^3 - 12x^3) - 21x^2 = 20x^4 + 23x^3 - 21x^2
\][/tex]

So, the correct answer is [tex]\(20x^4 + 23x^3 - 21x^2\)[/tex].

The answer is A. [tex]\(20x^4 + 23x^3 - 21x^2\)[/tex].

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