Answer :
Let's multiply the expressions [tex]\((4x^2 + 7x)\)[/tex] and [tex]\((5x^2 - 3x)\)[/tex] step-by-step:
1. Distribute [tex]\(4x^2\)[/tex] over [tex]\((5x^2 - 3x)\)[/tex]:
- Multiply [tex]\(4x^2\)[/tex] by [tex]\(5x^2\)[/tex]:
[tex]\[
4x^2 \times 5x^2 = 20x^4
\][/tex]
- Multiply [tex]\(4x^2\)[/tex] by [tex]\(-3x\)[/tex]:
[tex]\[
4x^2 \times (-3x) = -12x^3
\][/tex]
2. Distribute [tex]\(7x\)[/tex] over [tex]\((5x^2 - 3x)\)[/tex]:
- Multiply [tex]\(7x\)[/tex] by [tex]\(5x^2\)[/tex]:
[tex]\[
7x \times 5x^2 = 35x^3
\][/tex]
- Multiply [tex]\(7x\)[/tex] by [tex]\(-3x\)[/tex]:
[tex]\[
7x \times (-3x) = -21x^2
\][/tex]
3. Combine all terms:
Arrange all the products and then combine the like terms:
[tex]\[
20x^4 + (-12x^3) + 35x^3 + (-21x^2)
\][/tex]
- Combine the [tex]\(x^3\)[/tex] terms:
[tex]\[
-12x^3 + 35x^3 = 23x^3
\][/tex]
Thus, the resulting expression is:
[tex]\[
20x^4 + 23x^3 - 21x^2
\][/tex]
The correct answer is [tex]\(20x^4 + 23x^3 - 21x^2\)[/tex], which matches option B.
1. Distribute [tex]\(4x^2\)[/tex] over [tex]\((5x^2 - 3x)\)[/tex]:
- Multiply [tex]\(4x^2\)[/tex] by [tex]\(5x^2\)[/tex]:
[tex]\[
4x^2 \times 5x^2 = 20x^4
\][/tex]
- Multiply [tex]\(4x^2\)[/tex] by [tex]\(-3x\)[/tex]:
[tex]\[
4x^2 \times (-3x) = -12x^3
\][/tex]
2. Distribute [tex]\(7x\)[/tex] over [tex]\((5x^2 - 3x)\)[/tex]:
- Multiply [tex]\(7x\)[/tex] by [tex]\(5x^2\)[/tex]:
[tex]\[
7x \times 5x^2 = 35x^3
\][/tex]
- Multiply [tex]\(7x\)[/tex] by [tex]\(-3x\)[/tex]:
[tex]\[
7x \times (-3x) = -21x^2
\][/tex]
3. Combine all terms:
Arrange all the products and then combine the like terms:
[tex]\[
20x^4 + (-12x^3) + 35x^3 + (-21x^2)
\][/tex]
- Combine the [tex]\(x^3\)[/tex] terms:
[tex]\[
-12x^3 + 35x^3 = 23x^3
\][/tex]
Thus, the resulting expression is:
[tex]\[
20x^4 + 23x^3 - 21x^2
\][/tex]
The correct answer is [tex]\(20x^4 + 23x^3 - 21x^2\)[/tex], which matches option B.
