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Answer :
Let's solve the problem step-by-step by multiplying the expressions [tex]\((4x^2 + 7x)\)[/tex] and [tex]\((5x^2 - 3x)\)[/tex].
1. Distribute each term in the first expression to each term in the second expression:
[tex]\[
(4x^2 + 7x)(5x^2 - 3x) = 4x^2 \cdot 5x^2 + 4x^2 \cdot (-3x) + 7x \cdot 5x^2 + 7x \cdot (-3x)
\][/tex]
2. Multiply each pair of terms:
- [tex]\(4x^2 \cdot 5x^2 = 20x^4\)[/tex] (multiply the coefficients and add the exponents)
- [tex]\(4x^2 \cdot (-3x) = -12x^3\)[/tex] (multiply the coefficients and add the exponents)
- [tex]\(7x \cdot 5x^2 = 35x^3\)[/tex] (multiply the coefficients and add the exponents)
- [tex]\(7x \cdot (-3x) = -21x^2\)[/tex] (multiply the coefficients and add the exponents)
3. Combine the like terms:
[tex]\[
20x^4 + (-12x^3 + 35x^3) - 21x^2
\][/tex]
4. Simplify the expression:
- Combine the [tex]\(x^3\)[/tex] terms: [tex]\(-12x^3 + 35x^3 = 23x^3\)[/tex]
So, the expression simplifies to:
[tex]\[
20x^4 + 23x^3 - 21x^2
\][/tex]
Therefore, the final expression is [tex]\(20x^4 + 23x^3 - 21x^2\)[/tex].
Hence, the correct answer is:
[tex]\[
\text{A. } 20x^4 + 23x^3 - 21x^2
\][/tex]
1. Distribute each term in the first expression to each term in the second expression:
[tex]\[
(4x^2 + 7x)(5x^2 - 3x) = 4x^2 \cdot 5x^2 + 4x^2 \cdot (-3x) + 7x \cdot 5x^2 + 7x \cdot (-3x)
\][/tex]
2. Multiply each pair of terms:
- [tex]\(4x^2 \cdot 5x^2 = 20x^4\)[/tex] (multiply the coefficients and add the exponents)
- [tex]\(4x^2 \cdot (-3x) = -12x^3\)[/tex] (multiply the coefficients and add the exponents)
- [tex]\(7x \cdot 5x^2 = 35x^3\)[/tex] (multiply the coefficients and add the exponents)
- [tex]\(7x \cdot (-3x) = -21x^2\)[/tex] (multiply the coefficients and add the exponents)
3. Combine the like terms:
[tex]\[
20x^4 + (-12x^3 + 35x^3) - 21x^2
\][/tex]
4. Simplify the expression:
- Combine the [tex]\(x^3\)[/tex] terms: [tex]\(-12x^3 + 35x^3 = 23x^3\)[/tex]
So, the expression simplifies to:
[tex]\[
20x^4 + 23x^3 - 21x^2
\][/tex]
Therefore, the final expression is [tex]\(20x^4 + 23x^3 - 21x^2\)[/tex].
Hence, the correct answer is:
[tex]\[
\text{A. } 20x^4 + 23x^3 - 21x^2
\][/tex]
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