Answer :
Sure! Let's multiply the polynomials step by step.
We have the expression [tex]\((4x^2 + 7x)(5x^2 - 3x)\)[/tex]. To solve this, we need to apply the distributive property, also known as the FOIL method (First, Outer, Inner, Last).
1. First: Multiply the first terms from each binomial:
[tex]\[
4x^2 \cdot 5x^2 = 20x^4
\][/tex]
2. Outer: Multiply the outer terms:
[tex]\[
4x^2 \cdot (-3x) = -12x^3
\][/tex]
3. Inner: Multiply the inner terms:
[tex]\[
7x \cdot 5x^2 = 35x^3
\][/tex]
4. Last: Multiply the last terms:
[tex]\[
7x \cdot (-3x) = -21x^2
\][/tex]
Now, let's combine the like terms:
- Combine the [tex]\(x^3\)[/tex] terms:
[tex]\[
-12x^3 + 35x^3 = 23x^3
\][/tex]
As a result, the expression simplifies to:
[tex]\[
20x^4 + 23x^3 - 21x^2
\][/tex]
So, the correct answer is B. [tex]\(20x^4 + 23x^3 - 21x^2\)[/tex].
We have the expression [tex]\((4x^2 + 7x)(5x^2 - 3x)\)[/tex]. To solve this, we need to apply the distributive property, also known as the FOIL method (First, Outer, Inner, Last).
1. First: Multiply the first terms from each binomial:
[tex]\[
4x^2 \cdot 5x^2 = 20x^4
\][/tex]
2. Outer: Multiply the outer terms:
[tex]\[
4x^2 \cdot (-3x) = -12x^3
\][/tex]
3. Inner: Multiply the inner terms:
[tex]\[
7x \cdot 5x^2 = 35x^3
\][/tex]
4. Last: Multiply the last terms:
[tex]\[
7x \cdot (-3x) = -21x^2
\][/tex]
Now, let's combine the like terms:
- Combine the [tex]\(x^3\)[/tex] terms:
[tex]\[
-12x^3 + 35x^3 = 23x^3
\][/tex]
As a result, the expression simplifies to:
[tex]\[
20x^4 + 23x^3 - 21x^2
\][/tex]
So, the correct answer is B. [tex]\(20x^4 + 23x^3 - 21x^2\)[/tex].
