Answer :
To solve the problem, we need to multiply the two polynomials: [tex]\((4x^2 + 7x)\)[/tex] and [tex]\((5x^2 - 3x)\)[/tex].
Here’s how you can do it step-by-step:
1. Multiply each term in the first polynomial by each term in the second polynomial:
- Multiply [tex]\(4x^2\)[/tex] by [tex]\(5x^2\)[/tex]:
[tex]\[
4x^2 \cdot 5x^2 = 20x^4
\][/tex]
- Multiply [tex]\(4x^2\)[/tex] by [tex]\(-3x\)[/tex]:
[tex]\[
4x^2 \cdot (-3x) = -12x^3
\][/tex]
- Multiply [tex]\(7x\)[/tex] by [tex]\(5x^2\)[/tex]:
[tex]\[
7x \cdot 5x^2 = 35x^3
\][/tex]
- Multiply [tex]\(7x\)[/tex] by [tex]\(-3x\)[/tex]:
[tex]\[
7x \cdot (-3x) = -21x^2
\][/tex]
2. Combine all of the results:
- From the above multiplication you have:
[tex]\[
20x^4 - 12x^3 + 35x^3 - 21x^2
\][/tex]
3. Simplify by combining like terms:
- Combine the [tex]\(x^3\)[/tex] terms:
[tex]\[
-12x^3 + 35x^3 = 23x^3
\][/tex]
4. Write the final expression:
- Combine all the terms to get:
[tex]\[
20x^4 + 23x^3 - 21x^2
\][/tex]
This matches the answer choice B: [tex]\(20x^4 + 23x^3 - 21x^2\)[/tex].
Here’s how you can do it step-by-step:
1. Multiply each term in the first polynomial by each term in the second polynomial:
- Multiply [tex]\(4x^2\)[/tex] by [tex]\(5x^2\)[/tex]:
[tex]\[
4x^2 \cdot 5x^2 = 20x^4
\][/tex]
- Multiply [tex]\(4x^2\)[/tex] by [tex]\(-3x\)[/tex]:
[tex]\[
4x^2 \cdot (-3x) = -12x^3
\][/tex]
- Multiply [tex]\(7x\)[/tex] by [tex]\(5x^2\)[/tex]:
[tex]\[
7x \cdot 5x^2 = 35x^3
\][/tex]
- Multiply [tex]\(7x\)[/tex] by [tex]\(-3x\)[/tex]:
[tex]\[
7x \cdot (-3x) = -21x^2
\][/tex]
2. Combine all of the results:
- From the above multiplication you have:
[tex]\[
20x^4 - 12x^3 + 35x^3 - 21x^2
\][/tex]
3. Simplify by combining like terms:
- Combine the [tex]\(x^3\)[/tex] terms:
[tex]\[
-12x^3 + 35x^3 = 23x^3
\][/tex]
4. Write the final expression:
- Combine all the terms to get:
[tex]\[
20x^4 + 23x^3 - 21x^2
\][/tex]
This matches the answer choice B: [tex]\(20x^4 + 23x^3 - 21x^2\)[/tex].
