Answer :
To multiply the two polynomials [tex]\((4x^2 + 7x)\)[/tex] and [tex]\((5x^2 - 3x)\)[/tex], we need to apply the distributive property. This means we'll multiply every term in the first polynomial by every term in the second polynomial and then combine like terms. Let's go through this step by step:
1. Multiply the first term of the first polynomial 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 by each term of the second polynomial:
- [tex]\(7x \cdot 5x^2 = 35x^3\)[/tex]
- [tex]\(7x \cdot (-3x) = -21x^2\)[/tex]
3. Combine all the terms we found:
- [tex]\(20x^4\)[/tex] (from the first set of products)
- [tex]\(-12x^3\)[/tex] and [tex]\(35x^3\)[/tex] (combine these to get [tex]\(23x^3\)[/tex])
- [tex]\(-21x^2\)[/tex]
4. Write the final polynomial by combining like terms:
- The polynomial resulting from this multiplication is [tex]\(20x^4 + 23x^3 - 21x^2\)[/tex].
So, the correct answer that matches this polynomial is:
A. [tex]\(20x^4 + 23x^3 - 21x^2\)[/tex]
1. Multiply the first term of the first polynomial 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 by each term of the second polynomial:
- [tex]\(7x \cdot 5x^2 = 35x^3\)[/tex]
- [tex]\(7x \cdot (-3x) = -21x^2\)[/tex]
3. Combine all the terms we found:
- [tex]\(20x^4\)[/tex] (from the first set of products)
- [tex]\(-12x^3\)[/tex] and [tex]\(35x^3\)[/tex] (combine these to get [tex]\(23x^3\)[/tex])
- [tex]\(-21x^2\)[/tex]
4. Write the final polynomial by combining like terms:
- The polynomial resulting from this multiplication is [tex]\(20x^4 + 23x^3 - 21x^2\)[/tex].
So, the correct answer that matches this polynomial is:
A. [tex]\(20x^4 + 23x^3 - 21x^2\)[/tex]
