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Answer :
To multiply the polynomials [tex]\((4x^2 + 7x)\)[/tex] and [tex]\((5x^2 - 3x)\)[/tex], we'll follow these steps:
1. Multiply each term from the first polynomial by each term in the second polynomial.
- First Terms: Multiply [tex]\(4x^2\)[/tex] by [tex]\(5x^2\)[/tex].
[tex]\[
4x^2 \times 5x^2 = 20x^4
\][/tex]
- Outer Terms: Multiply [tex]\(4x^2\)[/tex] by [tex]\(-3x\)[/tex].
[tex]\[
4x^2 \times -3x = -12x^3
\][/tex]
- Inner Terms: Multiply [tex]\(7x\)[/tex] by [tex]\(5x^2\)[/tex].
[tex]\[
7x \times 5x^2 = 35x^3
\][/tex]
- Last Terms: Multiply [tex]\(7x\)[/tex] by [tex]\(-3x\)[/tex].
[tex]\[
7x \times -3x = -21x^2
\][/tex]
2. Combine like terms.
- Combine the [tex]\(x^3\)[/tex] terms:
[tex]\[
-12x^3 + 35x^3 = 23x^3
\][/tex]
3. Write down the resulting polynomial.
The combined expression gives us:
[tex]\[
20x^4 + 23x^3 - 21x^2
\][/tex]
So, the final answer for the multiplication is [tex]\(\boxed{20x^4 + 23x^3 - 21x^2}\)[/tex].
Comparing to the given options, the correct answer is:
- A. [tex]\(20x^4 + 23x^3 - 21x^2\)[/tex]
1. Multiply each term from the first polynomial by each term in the second polynomial.
- First Terms: Multiply [tex]\(4x^2\)[/tex] by [tex]\(5x^2\)[/tex].
[tex]\[
4x^2 \times 5x^2 = 20x^4
\][/tex]
- Outer Terms: Multiply [tex]\(4x^2\)[/tex] by [tex]\(-3x\)[/tex].
[tex]\[
4x^2 \times -3x = -12x^3
\][/tex]
- Inner Terms: Multiply [tex]\(7x\)[/tex] by [tex]\(5x^2\)[/tex].
[tex]\[
7x \times 5x^2 = 35x^3
\][/tex]
- Last Terms: Multiply [tex]\(7x\)[/tex] by [tex]\(-3x\)[/tex].
[tex]\[
7x \times -3x = -21x^2
\][/tex]
2. Combine like terms.
- Combine the [tex]\(x^3\)[/tex] terms:
[tex]\[
-12x^3 + 35x^3 = 23x^3
\][/tex]
3. Write down the resulting polynomial.
The combined expression gives us:
[tex]\[
20x^4 + 23x^3 - 21x^2
\][/tex]
So, the final answer for the multiplication is [tex]\(\boxed{20x^4 + 23x^3 - 21x^2}\)[/tex].
Comparing to the given options, the correct answer is:
- A. [tex]\(20x^4 + 23x^3 - 21x^2\)[/tex]
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