High School

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What is the product of the expression?



[tex](-2x - 9y^2)(-4x - 3)[/tex]



A. [tex]-8x^2 - 6x - 36xy^2 - 27y^2[/tex]

B. [tex]-14x^2 - 36xy^2 + 27y^2[/tex]

C. [tex]8x^2 + 6x + 36xy^2 + 27y^2[/tex]

D. [tex]14x^2 + 36xy^2 + 27y^2[/tex]

Answer :

To find the product

$$
\left(-2x-9y^2\right)(-4x-3),
$$

we use the distributive property (also known as the FOIL method when multiplying two binomials). Here are the steps:

1. Multiply the first term in the first expression by the first term in the second expression:
$$
(-2x) \cdot (-4x) = 8x^2.
$$

2. Multiply the first term in the first expression by the second term in the second expression:
$$
(-2x) \cdot (-3) = 6x.
$$

3. Multiply the second term in the first expression by the first term in the second expression:
$$
(-9y^2) \cdot (-4x) = 36xy^2.
$$

4. Multiply the second term in the first expression by the second term in the second expression:
$$
(-9y^2) \cdot (-3) = 27y^2.
$$

After calculating these four products, add them together:

$$
8x^2 + 6x + 36xy^2 + 27y^2.
$$

Thus, the product is

$$
8x^2+6x+36xy^2+27y^2.
$$

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