Answer :
To find the product of the expression [tex]\((-2x - 9y^2)(-4x - 3)\)[/tex], we need to apply the distributive property, also known as the FOIL method (First, Outer, Inner, Last). Here's how you do it step by step:
1. First Terms: Multiply the first terms from each binomial:
[tex]\[
(-2x) \times (-4x) = 8x^2
\][/tex]
2. Outer Terms: Multiply the outer terms:
[tex]\[
(-2x) \times (-3) = 6x
\][/tex]
3. Inner Terms: Multiply the inner terms:
[tex]\[
(-9y^2) \times (-4x) = 36xy^2
\][/tex]
4. Last Terms: Multiply the last terms from each binomial:
[tex]\[
(-9y^2) \times (-3) = 27y^2
\][/tex]
Now, combine all the terms together to form the final expression:
[tex]\[
8x^2 + 6x + 36xy^2 + 27y^2
\][/tex]
The correct product of the expression [tex]\((-2x - 9y^2)(-4x - 3)\)[/tex] is:
[tex]\[
8x^2 + 6x + 36xy^2 + 27y^2
\][/tex]
This matches the choice [tex]\(8x^2 + 6x + 36xy^2 + 27y^2\)[/tex] from the given options.
1. First Terms: Multiply the first terms from each binomial:
[tex]\[
(-2x) \times (-4x) = 8x^2
\][/tex]
2. Outer Terms: Multiply the outer terms:
[tex]\[
(-2x) \times (-3) = 6x
\][/tex]
3. Inner Terms: Multiply the inner terms:
[tex]\[
(-9y^2) \times (-4x) = 36xy^2
\][/tex]
4. Last Terms: Multiply the last terms from each binomial:
[tex]\[
(-9y^2) \times (-3) = 27y^2
\][/tex]
Now, combine all the terms together to form the final expression:
[tex]\[
8x^2 + 6x + 36xy^2 + 27y^2
\][/tex]
The correct product of the expression [tex]\((-2x - 9y^2)(-4x - 3)\)[/tex] is:
[tex]\[
8x^2 + 6x + 36xy^2 + 27y^2
\][/tex]
This matches the choice [tex]\(8x^2 + 6x + 36xy^2 + 27y^2\)[/tex] from the given options.
