High School

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What is the product of the expression?

[tex]
\[
\left(-2x - 9y^2\right)(-4x - 3)
\]
[/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 :

Sure! Let's solve the problem step-by-step by expanding the expression [tex]\((-2x - 9y^2)(-4x - 3)\)[/tex].

### Step 1: Distribute each term from the first expression to each term in the second expression.

1. Distribute [tex]\(-2x\)[/tex]:

[tex]\[
(-2x) \times (-4x) = 8x^2
\][/tex]

[tex]\[
(-2x) \times (-3) = 6x
\][/tex]

2. Distribute [tex]\(-9y^2\)[/tex]:

[tex]\[
(-9y^2) \times (-4x) = 36xy^2
\][/tex]

[tex]\[
(-9y^2) \times (-3) = 27y^2
\][/tex]

### Step 2: Combine all the terms together.

Now, we'll add all the results from the distribution:

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

This is the expanded form of the product.

### Conclusion

The expanded product is:

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

This corresponds to the option:

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

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Rewritten by : Barada