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Answer :
To multiply the polynomials [tex]\((7x^2 + 5x + 7)\)[/tex] and [tex]\((4x - 6)\)[/tex], we will use the distributive property. This means multiplying each term in the first polynomial by each term in the second polynomial and then combining like terms.
1. Multiply each term in [tex]\(7x^2 + 5x + 7\)[/tex] by [tex]\(4x\)[/tex]:
- [tex]\(7x^2 \cdot 4x = 28x^3\)[/tex]
- [tex]\(5x \cdot 4x = 20x^2\)[/tex]
- [tex]\(7 \cdot 4x = 28x\)[/tex]
2. Multiply each term in [tex]\(7x^2 + 5x + 7\)[/tex] by [tex]\(-6\)[/tex]:
- [tex]\(7x^2 \cdot -6 = -42x^2\)[/tex]
- [tex]\(5x \cdot -6 = -30x\)[/tex]
- [tex]\(7 \cdot -6 = -42\)[/tex]
3. Combine the results from both multiplications:
- [tex]\(28x^3\)[/tex]
- [tex]\(20x^2 - 42x^2 = -22x^2\)[/tex]
- [tex]\(28x - 30x = -2x\)[/tex]
- [tex]\(-42\)[/tex]
4. Write the final polynomial:
- [tex]\(28x^3 - 22x^2 - 2x - 42\)[/tex]
Therefore, the product of the polynomials is [tex]\(28x^3 - 22x^2 - 2x - 42\)[/tex], which corresponds to option A.
1. Multiply each term in [tex]\(7x^2 + 5x + 7\)[/tex] by [tex]\(4x\)[/tex]:
- [tex]\(7x^2 \cdot 4x = 28x^3\)[/tex]
- [tex]\(5x \cdot 4x = 20x^2\)[/tex]
- [tex]\(7 \cdot 4x = 28x\)[/tex]
2. Multiply each term in [tex]\(7x^2 + 5x + 7\)[/tex] by [tex]\(-6\)[/tex]:
- [tex]\(7x^2 \cdot -6 = -42x^2\)[/tex]
- [tex]\(5x \cdot -6 = -30x\)[/tex]
- [tex]\(7 \cdot -6 = -42\)[/tex]
3. Combine the results from both multiplications:
- [tex]\(28x^3\)[/tex]
- [tex]\(20x^2 - 42x^2 = -22x^2\)[/tex]
- [tex]\(28x - 30x = -2x\)[/tex]
- [tex]\(-42\)[/tex]
4. Write the final polynomial:
- [tex]\(28x^3 - 22x^2 - 2x - 42\)[/tex]
Therefore, the product of the polynomials is [tex]\(28x^3 - 22x^2 - 2x - 42\)[/tex], which corresponds to option A.
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