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Answer :
Let's solve the problem step-by-step by simplifying [tex]\((-2x - 8y^2)(-4x - 3)\)[/tex] using the distributive property.
1. Distribute [tex]\(-2x\)[/tex] to each term in [tex]\((-4x - 3)\)[/tex]:
[tex]\[
-2x \times -4x = 8x^2
\][/tex]
[tex]\[
-2x \times -3 = 6x
\][/tex]
So, distributing [tex]\(-2x\)[/tex] gives us [tex]\(8x^2 + 6x\)[/tex].
2. Distribute [tex]\(-8y^2\)[/tex] to each term in [tex]\((-4x - 3)\)[/tex]:
[tex]\[
-8y^2 \times -4x = 32xy^2
\][/tex]
[tex]\[
-8y^2 \times -3 = 24y^2
\][/tex]
So, distributing [tex]\(-8y^2\)[/tex] gives us [tex]\(32xy^2 + 24y^2\)[/tex].
3. Combine all the terms together:
When you put together all the terms from the distribution steps, you get:
[tex]\[
8x^2 + 6x + 32xy^2 + 24y^2
\][/tex]
The final simplified product of the expression [tex]\((-2x - 8y^2)(-4x - 3)\)[/tex] is [tex]\(8x^2 + 6x + 32xy^2 + 24y^2\)[/tex].
1. Distribute [tex]\(-2x\)[/tex] to each term in [tex]\((-4x - 3)\)[/tex]:
[tex]\[
-2x \times -4x = 8x^2
\][/tex]
[tex]\[
-2x \times -3 = 6x
\][/tex]
So, distributing [tex]\(-2x\)[/tex] gives us [tex]\(8x^2 + 6x\)[/tex].
2. Distribute [tex]\(-8y^2\)[/tex] to each term in [tex]\((-4x - 3)\)[/tex]:
[tex]\[
-8y^2 \times -4x = 32xy^2
\][/tex]
[tex]\[
-8y^2 \times -3 = 24y^2
\][/tex]
So, distributing [tex]\(-8y^2\)[/tex] gives us [tex]\(32xy^2 + 24y^2\)[/tex].
3. Combine all the terms together:
When you put together all the terms from the distribution steps, you get:
[tex]\[
8x^2 + 6x + 32xy^2 + 24y^2
\][/tex]
The final simplified product of the expression [tex]\((-2x - 8y^2)(-4x - 3)\)[/tex] is [tex]\(8x^2 + 6x + 32xy^2 + 24y^2\)[/tex].
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