Answer :
Sure! Let's multiply the two polynomials step by step:
[tex]\[
(4x^2 + 7x)(5x^2 - 3x)
\][/tex]
We will use the distributive property (also known as the FOIL method for binomials) to multiply each term in the first polynomial by each term in the second polynomial.
### Step 1: Multiply each term in the first polynomial by each term in the second polynomial
1. Multiply [tex]\(4x^2\)[/tex] by [tex]\(5x^2\)[/tex]:
[tex]\[
4x^2 \cdot 5x^2 = 20x^4
\][/tex]
2. Multiply [tex]\(4x^2\)[/tex] by [tex]\(-3x\)[/tex]:
[tex]\[
4x^2 \cdot (-3x) = -12x^3
\][/tex]
3. Multiply [tex]\(7x\)[/tex] by [tex]\(5x^2\)[/tex]:
[tex]\[
7x \cdot 5x^2 = 35x^3
\][/tex]
4. Multiply [tex]\(7x\)[/tex] by [tex]\(-3x\)[/tex]:
[tex]\[
7x \cdot (-3x) = -21x^2
\][/tex]
### Step 2: Combine all the products
[tex]\[
20x^4 - 12x^3 + 35x^3 - 21x^2
\][/tex]
### Step 3: Combine like terms
Combine the [tex]\(x^3\)[/tex] terms:
[tex]\[
-12x^3 + 35x^3 = 23x^3
\][/tex]
So our final expression is:
[tex]\[
20x^4 + 23x^3 - 21x^2
\][/tex]
### Conclusion
The correct answer is:
B. [tex]\(20x^4 + 23x^3 - 21x^2\)[/tex]
This matches the given choices.
[tex]\[
(4x^2 + 7x)(5x^2 - 3x)
\][/tex]
We will use the distributive property (also known as the FOIL method for binomials) to multiply each term in the first polynomial by each term in the second polynomial.
### Step 1: Multiply each term in the first polynomial by each term in the second polynomial
1. Multiply [tex]\(4x^2\)[/tex] by [tex]\(5x^2\)[/tex]:
[tex]\[
4x^2 \cdot 5x^2 = 20x^4
\][/tex]
2. Multiply [tex]\(4x^2\)[/tex] by [tex]\(-3x\)[/tex]:
[tex]\[
4x^2 \cdot (-3x) = -12x^3
\][/tex]
3. Multiply [tex]\(7x\)[/tex] by [tex]\(5x^2\)[/tex]:
[tex]\[
7x \cdot 5x^2 = 35x^3
\][/tex]
4. Multiply [tex]\(7x\)[/tex] by [tex]\(-3x\)[/tex]:
[tex]\[
7x \cdot (-3x) = -21x^2
\][/tex]
### Step 2: Combine all the products
[tex]\[
20x^4 - 12x^3 + 35x^3 - 21x^2
\][/tex]
### Step 3: Combine like terms
Combine the [tex]\(x^3\)[/tex] terms:
[tex]\[
-12x^3 + 35x^3 = 23x^3
\][/tex]
So our final expression is:
[tex]\[
20x^4 + 23x^3 - 21x^2
\][/tex]
### Conclusion
The correct answer is:
B. [tex]\(20x^4 + 23x^3 - 21x^2\)[/tex]
This matches the given choices.
