Answer :
To solve the multiplication of the polynomials [tex]\((4x^2 + 7x)(5x^2 - 3x)\)[/tex], we will use the distributive property to multiply each term in the first polynomial by each term in the second polynomial.
Let's go through it step-by-step:
1. Multiply the first term of the first polynomial, [tex]\(4x^2\)[/tex], by each term of the second polynomial:
- [tex]\(4x^2 \cdot 5x^2 = 20x^4\)[/tex]
- [tex]\(4x^2 \cdot (-3x) = -12x^3\)[/tex]
2. Multiply the second term of the first polynomial, [tex]\(7x\)[/tex], by each term of the second polynomial:
- [tex]\(7x \cdot 5x^2 = 35x^3\)[/tex]
- [tex]\(7x \cdot (-3x) = -21x^2\)[/tex]
3. Now, combine all these results:
[tex]\[
20x^4 + (-12x^3) + 35x^3 + (-21x^2)
\][/tex]
4. Combine like terms:
- [tex]\(20x^4\)[/tex] (no like terms for [tex]\(x^4\)[/tex])
- Combine [tex]\(x^3\)[/tex] terms: [tex]\(-12x^3 + 35x^3 = 23x^3\)[/tex]
- The [tex]\(x^2\)[/tex] term remains: [tex]\(-21x^2\)[/tex]
5. Put it all together:
[tex]\[
20x^4 + 23x^3 - 21x^2
\][/tex]
So, the correct answer is:
C. [tex]\(20x^4 + 23x^3 - 21x^2\)[/tex]
Let's go through it step-by-step:
1. Multiply the first term of the first polynomial, [tex]\(4x^2\)[/tex], by each term of the second polynomial:
- [tex]\(4x^2 \cdot 5x^2 = 20x^4\)[/tex]
- [tex]\(4x^2 \cdot (-3x) = -12x^3\)[/tex]
2. Multiply the second term of the first polynomial, [tex]\(7x\)[/tex], by each term of the second polynomial:
- [tex]\(7x \cdot 5x^2 = 35x^3\)[/tex]
- [tex]\(7x \cdot (-3x) = -21x^2\)[/tex]
3. Now, combine all these results:
[tex]\[
20x^4 + (-12x^3) + 35x^3 + (-21x^2)
\][/tex]
4. Combine like terms:
- [tex]\(20x^4\)[/tex] (no like terms for [tex]\(x^4\)[/tex])
- Combine [tex]\(x^3\)[/tex] terms: [tex]\(-12x^3 + 35x^3 = 23x^3\)[/tex]
- The [tex]\(x^2\)[/tex] term remains: [tex]\(-21x^2\)[/tex]
5. Put it all together:
[tex]\[
20x^4 + 23x^3 - 21x^2
\][/tex]
So, the correct answer is:
C. [tex]\(20x^4 + 23x^3 - 21x^2\)[/tex]
