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].
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].
