Answer :
Sure! Let's find the product of the expression [tex]\((-2x - 9y^2)(-4x - 3)\)[/tex] step-by-step:
1. Distribute each term: We'll multiply each term in the first expression by each term in the second expression.
2. Calculate the products:
- First, multiply [tex]\(-2x\)[/tex] by [tex]\(-4x\)[/tex]:
[tex]\[
(-2x) \times (-4x) = 8x^2
\][/tex]
- Then, multiply [tex]\(-2x\)[/tex] by [tex]\(-3\)[/tex]:
[tex]\[
(-2x) \times (-3) = 6x
\][/tex]
- Next, multiply [tex]\(-9y^2\)[/tex] by [tex]\(-4x\)[/tex]:
[tex]\[
(-9y^2) \times (-4x) = 36xy^2
\][/tex]
- Finally, multiply [tex]\(-9y^2\)[/tex] by [tex]\(-3\)[/tex]:
[tex]\[
(-9y^2) \times (-3) = 27y^2
\][/tex]
3. Combine all the terms:
- Collect all the results from the multiplications:
[tex]\[
8x^2 + 6x + 36xy^2 + 27y^2
\][/tex]
The expression for the product is [tex]\(8x^2 + 6x + 36xy^2 + 27y^2\)[/tex].
Looking at the given multiple-choice options, the correct answer is:
[tex]\[
8x^2 + 6x + 36xy^2 + 27y^2
\][/tex]
This matches the third option provided:
[tex]\[
8 x^2 + 6 x + 36 x y^2 + 27 y^2
\][/tex]
1. Distribute each term: We'll multiply each term in the first expression by each term in the second expression.
2. Calculate the products:
- First, multiply [tex]\(-2x\)[/tex] by [tex]\(-4x\)[/tex]:
[tex]\[
(-2x) \times (-4x) = 8x^2
\][/tex]
- Then, multiply [tex]\(-2x\)[/tex] by [tex]\(-3\)[/tex]:
[tex]\[
(-2x) \times (-3) = 6x
\][/tex]
- Next, multiply [tex]\(-9y^2\)[/tex] by [tex]\(-4x\)[/tex]:
[tex]\[
(-9y^2) \times (-4x) = 36xy^2
\][/tex]
- Finally, multiply [tex]\(-9y^2\)[/tex] by [tex]\(-3\)[/tex]:
[tex]\[
(-9y^2) \times (-3) = 27y^2
\][/tex]
3. Combine all the terms:
- Collect all the results from the multiplications:
[tex]\[
8x^2 + 6x + 36xy^2 + 27y^2
\][/tex]
The expression for the product is [tex]\(8x^2 + 6x + 36xy^2 + 27y^2\)[/tex].
Looking at the given multiple-choice options, the correct answer is:
[tex]\[
8x^2 + 6x + 36xy^2 + 27y^2
\][/tex]
This matches the third option provided:
[tex]\[
8 x^2 + 6 x + 36 x y^2 + 27 y^2
\][/tex]
