Answer :
To multiply the expressions [tex]\((4x^2 + 7x)\)[/tex] and [tex]\((5x^2 - 3x)\)[/tex], we will use the distributive property, also known as the FOIL method when dealing with binomials.
Here’s how you can do it step-by-step:
1. Multiply the first terms:
[tex]\[
4x^2 \times 5x^2 = 20x^4
\][/tex]
2. Multiply the outer terms:
[tex]\[
4x^2 \times (-3x) = -12x^3
\][/tex]
3. Multiply the inner terms:
[tex]\[
7x \times 5x^2 = 35x^3
\][/tex]
4. Multiply the last terms:
[tex]\[
7x \times (-3x) = -21x^2
\][/tex]
5. Combine like terms:
Now add all these results together:
[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]
So, the final expanded expression is:
[tex]\[
20x^4 + 23x^3 - 21x^2
\][/tex]
After checking the options, the correct option is:
- B. [tex]\(20x^4 + 23x^3 - 21x^2\)[/tex]
This is the result of multiplying the given expressions.
Here’s how you can do it step-by-step:
1. Multiply the first terms:
[tex]\[
4x^2 \times 5x^2 = 20x^4
\][/tex]
2. Multiply the outer terms:
[tex]\[
4x^2 \times (-3x) = -12x^3
\][/tex]
3. Multiply the inner terms:
[tex]\[
7x \times 5x^2 = 35x^3
\][/tex]
4. Multiply the last terms:
[tex]\[
7x \times (-3x) = -21x^2
\][/tex]
5. Combine like terms:
Now add all these results together:
[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]
So, the final expanded expression is:
[tex]\[
20x^4 + 23x^3 - 21x^2
\][/tex]
After checking the options, the correct option is:
- B. [tex]\(20x^4 + 23x^3 - 21x^2\)[/tex]
This is the result of multiplying the given expressions.
