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Answer :
To solve the problem of multiplying [tex]\((4x^2 + 7x)(5x^2 - 3x)\)[/tex], we will use the distributive property, often known as the FOIL method, to expand the expression. Here are the steps:
1. First: Multiply the first terms of each binomial.
[tex]\[
(4x^2) \times (5x^2) = 20x^4
\][/tex]
2. Outer: Multiply the outer terms of the binomial.
[tex]\[
(4x^2) \times (-3x) = -12x^3
\][/tex]
3. Inner: Multiply the inner terms of the binomial.
[tex]\[
(7x) \times (5x^2) = 35x^3
\][/tex]
4. Last: Multiply the last terms of each binomial.
[tex]\[
(7x) \times (-3x) = -21x^2
\][/tex]
Now, let's combine all these results:
- Start with the [tex]\(x^4\)[/tex] term: [tex]\(20x^4\)[/tex].
- Combine the [tex]\(x^3\)[/tex] terms: [tex]\(-12x^3 + 35x^3 = 23x^3\)[/tex].
- Then, the [tex]\(x^2\)[/tex] term: [tex]\(-21x^2\)[/tex].
Putting it all together, the expanded expression is:
[tex]\[
20x^4 + 23x^3 - 21x^2
\][/tex]
This matches option C: [tex]\(20x^4 + 23x^3 - 21x^2\)[/tex].
1. First: Multiply the first terms of each binomial.
[tex]\[
(4x^2) \times (5x^2) = 20x^4
\][/tex]
2. Outer: Multiply the outer terms of the binomial.
[tex]\[
(4x^2) \times (-3x) = -12x^3
\][/tex]
3. Inner: Multiply the inner terms of the binomial.
[tex]\[
(7x) \times (5x^2) = 35x^3
\][/tex]
4. Last: Multiply the last terms of each binomial.
[tex]\[
(7x) \times (-3x) = -21x^2
\][/tex]
Now, let's combine all these results:
- Start with the [tex]\(x^4\)[/tex] term: [tex]\(20x^4\)[/tex].
- Combine the [tex]\(x^3\)[/tex] terms: [tex]\(-12x^3 + 35x^3 = 23x^3\)[/tex].
- Then, the [tex]\(x^2\)[/tex] term: [tex]\(-21x^2\)[/tex].
Putting it all together, the expanded expression is:
[tex]\[
20x^4 + 23x^3 - 21x^2
\][/tex]
This matches option C: [tex]\(20x^4 + 23x^3 - 21x^2\)[/tex].
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