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Answer :
To solve the problem of multiplying the polynomials [tex]\((4x^2 + 7x)\)[/tex] and [tex]\((5x^2 - 3x)\)[/tex], we can follow these steps:
1. Distribute each term in the first polynomial across each term in the second polynomial:
- Multiply [tex]\(4x^2\)[/tex] by each term in [tex]\((5x^2 - 3x)\)[/tex]:
- [tex]\(4x^2 \times 5x^2 = 20x^4\)[/tex]
- [tex]\(4x^2 \times -3x = -12x^3\)[/tex]
- Multiply [tex]\(7x\)[/tex] by each term in [tex]\((5x^2 - 3x)\)[/tex]:
- [tex]\(7x \times 5x^2 = 35x^3\)[/tex]
- [tex]\(7x \times -3x = -21x^2\)[/tex]
2. Combine like terms:
- The terms obtained from the distribution are: [tex]\(20x^4\)[/tex], [tex]\(-12x^3\)[/tex], [tex]\(35x^3\)[/tex], and [tex]\(-21x^2\)[/tex].
- Combine the [tex]\(x^3\)[/tex] terms: [tex]\(-12x^3 + 35x^3 = 23x^3\)[/tex].
3. Write the final result:
Combining all terms, the expanded form of the polynomial is:
[tex]\[
20x^4 + 23x^3 - 21x^2
\][/tex]
So, the correct answer is:
B. [tex]\(20x^4 + 23x^3 - 21x^2\)[/tex]
1. Distribute each term in the first polynomial across each term in the second polynomial:
- Multiply [tex]\(4x^2\)[/tex] by each term in [tex]\((5x^2 - 3x)\)[/tex]:
- [tex]\(4x^2 \times 5x^2 = 20x^4\)[/tex]
- [tex]\(4x^2 \times -3x = -12x^3\)[/tex]
- Multiply [tex]\(7x\)[/tex] by each term in [tex]\((5x^2 - 3x)\)[/tex]:
- [tex]\(7x \times 5x^2 = 35x^3\)[/tex]
- [tex]\(7x \times -3x = -21x^2\)[/tex]
2. Combine like terms:
- The terms obtained from the distribution are: [tex]\(20x^4\)[/tex], [tex]\(-12x^3\)[/tex], [tex]\(35x^3\)[/tex], and [tex]\(-21x^2\)[/tex].
- Combine the [tex]\(x^3\)[/tex] terms: [tex]\(-12x^3 + 35x^3 = 23x^3\)[/tex].
3. Write the final result:
Combining all terms, the expanded form of the polynomial is:
[tex]\[
20x^4 + 23x^3 - 21x^2
\][/tex]
So, the correct answer is:
B. [tex]\(20x^4 + 23x^3 - 21x^2\)[/tex]
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