Which of the following expressions is equivalent to $(-7x^3 + 9x^2 - 3)(-2x^2 - 5x + 6)$?

A) $-14x^5 + 19x^4 - 6x^2 - 35x^3 + 45x^2 - 15$

B) $14x^5 - 19x^4 + 6x^2 + 35x^3 - 45x^2 + 15$

C) $-14x^5 + 19x^4 - 6x^2 + 35x^3 - 45x^2 + 15$

D) $14x^5 - 19x^4 + 6x^2 - 35x^3 + 45x^2 - 15$

Question

13-03-2024
Mathematics

High School

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Which of the following expressions is equivalent to $(-7x^3 + 9x^2 - 3)(-2x^2 - 5x + 6)$?

A) $-14x^5 + 19x^4 - 6x^2 - 35x^3 + 45x^2 - 15$

B) $14x^5 - 19x^4 + 6x^2 + 35x^3 - 45x^2 + 15$

C) $-14x^5 + 19x^4 - 6x^2 + 35x^3 - 45x^2 + 15$

D) $14x^5 - 19x^4 + 6x^2 - 35x^3 + 45x^2 - 15$

Answer :

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hemalatharaja201 hemalatharaja201 · Answer 1 · 2024-03-26T04:38:18-04:00

Final answer:

The process involves using the distributive property of multiplication over addition to expand the expression. You multiply each term in the first polynomial by each in the second, and add up these results. However, none of the presented options match the result.

Explanation:

The question is asking which of the given expressions is equivalent to multiplying (-7x^3 + 9x^2 - 3) and (-2x^2 - 5x + 6). To solve this, we can use the distributive property of multiplication, which involves multiplying each term in the first polynomials (-7x^3, 9x^2, -3) by each term in the second polynomial (-2x^2, -5x, 6) individually, then adding the results.

Step 1: Multiply -7x^3 by each term in the second polynomial and add these results together. You will get 14x^5 + 35x^4 - 42x^3.

Step 2: Multiply 9x^2 by each term in the second polynomial and add these results to the previous step. You will get 14x^5 + 35x^4 - 42x^3 - 18x^4 - 45x^3 + 54x^2.

Step 3: Multiply -3 by each term in the second polynomial and add these results to the previous step. You will get 14x^5 + 35x^4 - 42x^3 - 18x^4 - 45x^3 + 54x^2 + 6x^2 + 15x - 18.

Next, you should simplify the expression by combining like terms. Unfortunately, none of the given options matches with the result of our calculations.

Learn more about Polynomial Multiplication here:

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Which of the following expressions is equivalent to \((-7x^3 + 9x^2 - 3)(-2x^2 - 5x + 6)\)?A) \(-14x^5 + 19x^4 - 6x^2 - 35x^3 + 45x^2 - 15\)B) \(14x^5 - 19x^4 + 6x^2 + 35x^3 - 45x^2 + 15\)C) \(-14x^5 + 19x^4 - 6x^2 + 35x^3 - 45x^2 + 15\)D) \(14x^5 - 19x^4 + 6x^2 - 35x^3 + 45x^2 - 15\)

Answer :

Final answer:

Explanation:

Learn more about Polynomial Multiplication here:

Other Questions

Which of the following expressions is equivalent to \((-7x^3 + 9x^2 - 3)(-2x^2 - 5x + 6)\)?

A) \(-14x^5 + 19x^4 - 6x^2 - 35x^3 + 45x^2 - 15\)

B) \(14x^5 - 19x^4 + 6x^2 + 35x^3 - 45x^2 + 15\)

C) \(-14x^5 + 19x^4 - 6x^2 + 35x^3 - 45x^2 + 15\)

D) \(14x^5 - 19x^4 + 6x^2 - 35x^3 + 45x^2 - 15\)