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Answer :
To find the product [tex]\((-2x - 9y^2)(-4x - 3)\)[/tex], we can use the distributive property, also known as the FOIL method for binomials (First, Outer, Inner, Last). Let's expand the expression step-by-step:
1. First: Multiply the first terms in each binomial:
[tex]\[
(-2x) \times (-4x) = 8x^2
\][/tex]
2. Outer: Multiply the outer terms in the binomials:
[tex]\[
(-2x) \times (-3) = 6x
\][/tex]
3. Inner: Multiply the inner terms:
[tex]\[
(-9y^2) \times (-4x) = 36xy^2
\][/tex]
4. Last: Multiply the last terms in each binomial:
[tex]\[
(-9y^2) \times (-3) = 27y^2
\][/tex]
Finally, combine all these terms to get the expanded product:
[tex]\[
8x^2 + 6x + 36xy^2 + 27y^2
\][/tex]
Therefore, the product of [tex]\((-2x - 9y^2)(-4x - 3)\)[/tex] is [tex]\(8x^2 + 6x + 36xy^2 + 27y^2\)[/tex].
From the provided options, the correct one is:
[tex]\[8x^2 + 6x + 36xy^2 + 27y^2\][/tex]
1. First: Multiply the first terms in each binomial:
[tex]\[
(-2x) \times (-4x) = 8x^2
\][/tex]
2. Outer: Multiply the outer terms in the binomials:
[tex]\[
(-2x) \times (-3) = 6x
\][/tex]
3. Inner: Multiply the inner terms:
[tex]\[
(-9y^2) \times (-4x) = 36xy^2
\][/tex]
4. Last: Multiply the last terms in each binomial:
[tex]\[
(-9y^2) \times (-3) = 27y^2
\][/tex]
Finally, combine all these terms to get the expanded product:
[tex]\[
8x^2 + 6x + 36xy^2 + 27y^2
\][/tex]
Therefore, the product of [tex]\((-2x - 9y^2)(-4x - 3)\)[/tex] is [tex]\(8x^2 + 6x + 36xy^2 + 27y^2\)[/tex].
From the provided options, the correct one is:
[tex]\[8x^2 + 6x + 36xy^2 + 27y^2\][/tex]
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