Answer :
To find the product of [tex]\((-2x - 9y^2)(-4x - 3)\)[/tex], let's multiply these expressions using the distributive property, also known as the FOIL method when dealing with binomials.
Here's a step-by-step breakdown:
1. Multiply each term in the first binomial by each term in the second binomial:
- First, multiply [tex]\(-2x\)[/tex] by [tex]\(-4x\)[/tex]:
[tex]\[
(-2x) \cdot (-4x) = 8x^2
\][/tex]
- Next, multiply [tex]\(-2x\)[/tex] by [tex]\(-3\)[/tex]:
[tex]\[
(-2x) \cdot (-3) = 6x
\][/tex]
- Then, multiply [tex]\(-9y^2\)[/tex] by [tex]\(-4x\)[/tex]:
[tex]\[
(-9y^2) \cdot (-4x) = 36xy^2
\][/tex]
- Finally, multiply [tex]\(-9y^2\)[/tex] by [tex]\(-3\)[/tex]:
[tex]\[
(-9y^2) \cdot (-3) = 27y^2
\][/tex]
2. Combine all these products:
[tex]\[
8x^2 + 6x + 36xy^2 + 27y^2
\][/tex]
This gives us the final expanded expression. Therefore, the product of [tex]\((-2x - 9y^2)(-4x - 3)\)[/tex] is:
[tex]\[
8x^2 + 6x + 36xy^2 + 27y^2
\][/tex]
The answer is [tex]\(8x^2 + 6x + 36xy^2 + 27y^2\)[/tex].
Here's a step-by-step breakdown:
1. Multiply each term in the first binomial by each term in the second binomial:
- First, multiply [tex]\(-2x\)[/tex] by [tex]\(-4x\)[/tex]:
[tex]\[
(-2x) \cdot (-4x) = 8x^2
\][/tex]
- Next, multiply [tex]\(-2x\)[/tex] by [tex]\(-3\)[/tex]:
[tex]\[
(-2x) \cdot (-3) = 6x
\][/tex]
- Then, multiply [tex]\(-9y^2\)[/tex] by [tex]\(-4x\)[/tex]:
[tex]\[
(-9y^2) \cdot (-4x) = 36xy^2
\][/tex]
- Finally, multiply [tex]\(-9y^2\)[/tex] by [tex]\(-3\)[/tex]:
[tex]\[
(-9y^2) \cdot (-3) = 27y^2
\][/tex]
2. Combine all these products:
[tex]\[
8x^2 + 6x + 36xy^2 + 27y^2
\][/tex]
This gives us the final expanded expression. Therefore, the product of [tex]\((-2x - 9y^2)(-4x - 3)\)[/tex] is:
[tex]\[
8x^2 + 6x + 36xy^2 + 27y^2
\][/tex]
The answer is [tex]\(8x^2 + 6x + 36xy^2 + 27y^2\)[/tex].
