Answer :
To solve the problem [tex]\((4x^2 + 7x)(5x^2 - 3x)\)[/tex], we need to expand the expression using the distributive property, also known as the FOIL method, which stands for First, Outer, Inner, and Last terms.
Here's how it works:
1. First: Multiply the first terms in each binomial:
[tex]\[
4x^2 \cdot 5x^2 = 20x^4
\][/tex]
2. Outer: Multiply the outer terms:
[tex]\[
4x^2 \cdot (-3x) = -12x^3
\][/tex]
3. Inner: Multiply the inner terms:
[tex]\[
7x \cdot 5x^2 = 35x^3
\][/tex]
4. Last: Multiply the last terms:
[tex]\[
7x \cdot (-3x) = -21x^2
\][/tex]
Next, we combine all these results together:
[tex]\[
20x^4 + (-12x^3) + 35x^3 - 21x^2
\][/tex]
Now, combine the like terms:
- Combine the [tex]\(x^3\)[/tex] terms:
[tex]\[
-12x^3 + 35x^3 = 23x^3
\][/tex]
Putting it all together, we get the final expanded expression:
[tex]\[
20x^4 + 23x^3 - 21x^2
\][/tex]
Therefore, the correct answer is B. [tex]\(20x^4 + 23x^3 - 21x^2\)[/tex].
Here's how it works:
1. First: Multiply the first terms in each binomial:
[tex]\[
4x^2 \cdot 5x^2 = 20x^4
\][/tex]
2. Outer: Multiply the outer terms:
[tex]\[
4x^2 \cdot (-3x) = -12x^3
\][/tex]
3. Inner: Multiply the inner terms:
[tex]\[
7x \cdot 5x^2 = 35x^3
\][/tex]
4. Last: Multiply the last terms:
[tex]\[
7x \cdot (-3x) = -21x^2
\][/tex]
Next, we combine all these results together:
[tex]\[
20x^4 + (-12x^3) + 35x^3 - 21x^2
\][/tex]
Now, combine the like terms:
- Combine the [tex]\(x^3\)[/tex] terms:
[tex]\[
-12x^3 + 35x^3 = 23x^3
\][/tex]
Putting it all together, we get the final expanded expression:
[tex]\[
20x^4 + 23x^3 - 21x^2
\][/tex]
Therefore, the correct answer is B. [tex]\(20x^4 + 23x^3 - 21x^2\)[/tex].
