Answer :
To multiply the expressions [tex]\((4x^2 + 7x)\)[/tex] and [tex]\((5x^2 - 3x)\)[/tex], we use the distributive property, often referred to as the FOIL method (First, Outer, Inner, Last) for binomials. Let's organize our steps clearly:
1. First Terms: Multiply the first terms of each expression:
[tex]\[
(4x^2) \times (5x^2) = 20x^4
\][/tex]
2. Outer Terms: Multiply the outer terms:
[tex]\[
(4x^2) \times (-3x) = -12x^3
\][/tex]
3. Inner Terms: Multiply the inner terms:
[tex]\[
(7x) \times (5x^2) = 35x^3
\][/tex]
4. Last Terms: Multiply the last terms:
[tex]\[
(7x) \times (-3x) = -21x^2
\][/tex]
5. Combine Like Terms: Now, let's combine all of these results:
[tex]\[
20x^4 + (-12x^3) + 35x^3 + (-21x^2)
\][/tex]
[tex]\[
= 20x^4 + (35x^3 - 12x^3) - 21x^2
\][/tex]
[tex]\[
= 20x^4 + 23x^3 - 21x^2
\][/tex]
Therefore, after performing these multiplications and combining like terms, the expanded result is [tex]\(20x^4 + 23x^3 - 21x^2\)[/tex].
The answer that matches this result is:
B. [tex]\(20x^4 + 23x^3 - 21x^2\)[/tex]
1. First Terms: Multiply the first terms of each expression:
[tex]\[
(4x^2) \times (5x^2) = 20x^4
\][/tex]
2. Outer Terms: Multiply the outer terms:
[tex]\[
(4x^2) \times (-3x) = -12x^3
\][/tex]
3. Inner Terms: Multiply the inner terms:
[tex]\[
(7x) \times (5x^2) = 35x^3
\][/tex]
4. Last Terms: Multiply the last terms:
[tex]\[
(7x) \times (-3x) = -21x^2
\][/tex]
5. Combine Like Terms: Now, let's combine all of these results:
[tex]\[
20x^4 + (-12x^3) + 35x^3 + (-21x^2)
\][/tex]
[tex]\[
= 20x^4 + (35x^3 - 12x^3) - 21x^2
\][/tex]
[tex]\[
= 20x^4 + 23x^3 - 21x^2
\][/tex]
Therefore, after performing these multiplications and combining like terms, the expanded result is [tex]\(20x^4 + 23x^3 - 21x^2\)[/tex].
The answer that matches this result is:
B. [tex]\(20x^4 + 23x^3 - 21x^2\)[/tex]
