Answer :
Let's multiply the two polynomials [tex]\((4x^2 + 7x)\)[/tex] and [tex]\((5x^2 - 3x)\)[/tex] step-by-step:
1. Distribute each term in the first polynomial to each term in the second polynomial:
[tex]\[
(4x^2 + 7x)(5x^2 - 3x)
= 4x^2 \cdot 5x^2 + 4x^2 \cdot (-3x) + 7x \cdot 5x^2 + 7x \cdot (-3x)
\][/tex]
2. Multiply each pair of terms:
- [tex]\(4x^2 \cdot 5x^2 = 20x^4\)[/tex]
- [tex]\(4x^2 \cdot (-3x) = -12x^3\)[/tex]
- [tex]\(7x \cdot 5x^2 = 35x^3\)[/tex]
- [tex]\(7x \cdot (-3x) = -21x^2\)[/tex]
3. Combine the resulting terms:
Now, we add the terms obtained:
- [tex]\(20x^4\)[/tex] is the only [tex]\(x^4\)[/tex] term.
- Combine the [tex]\(x^3\)[/tex] terms: [tex]\(-12x^3 + 35x^3 = 23x^3\)[/tex].
- [tex]\(-21x^2\)[/tex] is the only [tex]\(x^2\)[/tex] term.
4. Write the final expression:
[tex]\[
20x^4 + 23x^3 - 21x^2
\][/tex]
This matches option A: [tex]\(20x^4 + 23x^3 - 21x^2\)[/tex].
So, the correct answer is A. [tex]\(20x^4 + 23x^3 - 21x^2\)[/tex].
1. Distribute each term in the first polynomial to each term in the second polynomial:
[tex]\[
(4x^2 + 7x)(5x^2 - 3x)
= 4x^2 \cdot 5x^2 + 4x^2 \cdot (-3x) + 7x \cdot 5x^2 + 7x \cdot (-3x)
\][/tex]
2. Multiply each pair of terms:
- [tex]\(4x^2 \cdot 5x^2 = 20x^4\)[/tex]
- [tex]\(4x^2 \cdot (-3x) = -12x^3\)[/tex]
- [tex]\(7x \cdot 5x^2 = 35x^3\)[/tex]
- [tex]\(7x \cdot (-3x) = -21x^2\)[/tex]
3. Combine the resulting terms:
Now, we add the terms obtained:
- [tex]\(20x^4\)[/tex] is the only [tex]\(x^4\)[/tex] term.
- Combine the [tex]\(x^3\)[/tex] terms: [tex]\(-12x^3 + 35x^3 = 23x^3\)[/tex].
- [tex]\(-21x^2\)[/tex] is the only [tex]\(x^2\)[/tex] term.
4. Write the final expression:
[tex]\[
20x^4 + 23x^3 - 21x^2
\][/tex]
This matches option A: [tex]\(20x^4 + 23x^3 - 21x^2\)[/tex].
So, the correct answer is A. [tex]\(20x^4 + 23x^3 - 21x^2\)[/tex].
