Answer :
Sure! Let's solve the problem step-by-step by expanding the given expression [tex]\((-2x - 9y^2)(-4x - 3)\)[/tex].
1. Use the distributive property (FOIL method):
- Multiply each term in the first parenthesis by each term in the second parenthesis.
2. Calculate each multiplication:
- First, multiply [tex]\(-2x\)[/tex] by [tex]\(-4x\)[/tex]:
[tex]\[
(-2x)(-4x) = 8x^2
\][/tex]
- Then, multiply [tex]\(-2x\)[/tex] by [tex]\(-3\)[/tex]:
[tex]\[
(-2x)(-3) = 6x
\][/tex]
- Next, multiply [tex]\(-9y^2\)[/tex] by [tex]\(-4x\)[/tex]:
[tex]\[
(-9y^2)(-4x) = 36xy^2
\][/tex]
- Finally, multiply [tex]\(-9y^2\)[/tex] by [tex]\(-3\)[/tex]:
[tex]\[
(-9y^2)(-3) = 27y^2
\][/tex]
3. Combine all the terms together:
[tex]\[
8x^2 + 6x + 36xy^2 + 27y^2
\][/tex]
The product is [tex]\(8x^2 + 6x + 36xy^2 + 27y^2\)[/tex].
Looking at the options provided, the correct expression corresponds to:
[tex]\[ \text{Option } 8x^2 + 6x + 36xy^2 + 27y^2 \][/tex]
1. Use the distributive property (FOIL method):
- Multiply each term in the first parenthesis by each term in the second parenthesis.
2. Calculate each multiplication:
- First, multiply [tex]\(-2x\)[/tex] by [tex]\(-4x\)[/tex]:
[tex]\[
(-2x)(-4x) = 8x^2
\][/tex]
- Then, multiply [tex]\(-2x\)[/tex] by [tex]\(-3\)[/tex]:
[tex]\[
(-2x)(-3) = 6x
\][/tex]
- Next, multiply [tex]\(-9y^2\)[/tex] by [tex]\(-4x\)[/tex]:
[tex]\[
(-9y^2)(-4x) = 36xy^2
\][/tex]
- Finally, multiply [tex]\(-9y^2\)[/tex] by [tex]\(-3\)[/tex]:
[tex]\[
(-9y^2)(-3) = 27y^2
\][/tex]
3. Combine all the terms together:
[tex]\[
8x^2 + 6x + 36xy^2 + 27y^2
\][/tex]
The product is [tex]\(8x^2 + 6x + 36xy^2 + 27y^2\)[/tex].
Looking at the options provided, the correct expression corresponds to:
[tex]\[ \text{Option } 8x^2 + 6x + 36xy^2 + 27y^2 \][/tex]
