High School

What is the product of \((-2x-9y^2)(-4x-3)\)?

A. \(-8x^2 - 6x - 36xy^2 - 27y^2\)

B. \(-14x^2 - 36xy^2 + 27y^2\)

C. \(8x^2 + 6x + 36xy^2 + 27y^2\)

D. \(14x^2 + 36xy^2 + 27y^2\)

Answer :

Final answer:

The product of (-2x-9y²)(-4x-3) is 8x² + 6x + 36xy² + 27y². Therefore, option C is correct.

Explanation:

To find the product (-2x-9y²)(-4x-3), we can use the distributive property. We multiply each term in the first expression (-2x-9y²) by each term in the second expression (-4x-3) and then add the resulting products.

So, the product is:

-2x * -4x + (-2x * -3) + (-9y² * -4x) + (-9y² * -3)

Which simplifies to:

8x² + 6x + 36xy² + 27y²

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