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Answer :
Sure! Let's multiply the polynomials [tex]\((7x^2 + 5x + 7)\)[/tex] and [tex]\((4x - 6)\)[/tex] step by step.
We use the distributive property (also known as the FOIL method for binomials) to multiply each term in the first polynomial by each term in the second polynomial.
1. Multiply [tex]\(7x^2\)[/tex] by both terms in [tex]\(4x - 6\)[/tex]:
[tex]\(7x^2 \cdot 4x = 28x^3\)[/tex]
[tex]\(7x^2 \cdot (-6) = -42x^2\)[/tex]
2. Multiply [tex]\(5x\)[/tex] by both terms in [tex]\(4x - 6\)[/tex]:
[tex]\(5x \cdot 4x = 20x^2\)[/tex]
[tex]\(5x \cdot (-6) = -30x\)[/tex]
3. Multiply [tex]\(7\)[/tex] by both terms in [tex]\(4x - 6\)[/tex]:
[tex]\(7 \cdot 4x = 28x\)[/tex]
[tex]\(7 \cdot (-6) = -42\)[/tex]
Now, combine all the terms:
[tex]\[ 28x^3 + (-42x^2) + 20x^2 + (-30x) + 28x + (-42) \][/tex]
Combine like terms:
[tex]\[ 28x^3 + (-42x^2 + 20x^2) + (-30x + 28x) + (-42) \][/tex]
[tex]\[ 28x^3 - 22x^2 - 2x - 42 \][/tex]
So, the result of multiplying the polynomials [tex]\((7x^2 + 5x + 7)\)[/tex] and [tex]\((4x - 6)\)[/tex] is:
[tex]\[ 28x^3 - 22x^2 - 2x - 42 \][/tex]
Therefore, the correct answer is:
[tex]\[ \boxed{A. 28x^3 - 22x^2 - 2x - 42} \][/tex]
We use the distributive property (also known as the FOIL method for binomials) to multiply each term in the first polynomial by each term in the second polynomial.
1. Multiply [tex]\(7x^2\)[/tex] by both terms in [tex]\(4x - 6\)[/tex]:
[tex]\(7x^2 \cdot 4x = 28x^3\)[/tex]
[tex]\(7x^2 \cdot (-6) = -42x^2\)[/tex]
2. Multiply [tex]\(5x\)[/tex] by both terms in [tex]\(4x - 6\)[/tex]:
[tex]\(5x \cdot 4x = 20x^2\)[/tex]
[tex]\(5x \cdot (-6) = -30x\)[/tex]
3. Multiply [tex]\(7\)[/tex] by both terms in [tex]\(4x - 6\)[/tex]:
[tex]\(7 \cdot 4x = 28x\)[/tex]
[tex]\(7 \cdot (-6) = -42\)[/tex]
Now, combine all the terms:
[tex]\[ 28x^3 + (-42x^2) + 20x^2 + (-30x) + 28x + (-42) \][/tex]
Combine like terms:
[tex]\[ 28x^3 + (-42x^2 + 20x^2) + (-30x + 28x) + (-42) \][/tex]
[tex]\[ 28x^3 - 22x^2 - 2x - 42 \][/tex]
So, the result of multiplying the polynomials [tex]\((7x^2 + 5x + 7)\)[/tex] and [tex]\((4x - 6)\)[/tex] is:
[tex]\[ 28x^3 - 22x^2 - 2x - 42 \][/tex]
Therefore, the correct answer is:
[tex]\[ \boxed{A. 28x^3 - 22x^2 - 2x - 42} \][/tex]
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