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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 for binomials. Here's a detailed step-by-step solution:
1. Distribute each term in the first expression to every term in the second expression. This involves multiplying each term in [tex]\((-2x - 9y^2)\)[/tex] by each term in [tex]\((-4x - 3)\)[/tex].
2. Multiply the first term of the first expression with each term of the second expression:
- Multiply [tex]\(-2x\)[/tex] with [tex]\(-4x\)[/tex]:
[tex]\[
(-2x) \times (-4x) = 8x^2
\][/tex]
- Multiply [tex]\(-2x\)[/tex] with [tex]\(-3\)[/tex]:
[tex]\[
(-2x) \times (-3) = 6x
\][/tex]
3. Multiply the second term of the first expression with each term of the second expression:
- Multiply [tex]\(-9y^2\)[/tex] with [tex]\(-4x\)[/tex]:
[tex]\[
(-9y^2) \times (-4x) = 36xy^2
\][/tex]
- Multiply [tex]\(-9y^2\)[/tex] with [tex]\(-3\)[/tex]:
[tex]\[
(-9y^2) \times (-3) = 27y^2
\][/tex]
4. Combine all these results to get the expanded product:
[tex]\[
8x^2 + 6x + 36xy^2 + 27y^2
\][/tex]
So, the product of the expression [tex]\((-2x - 9y^2)(-4x - 3)\)[/tex] is [tex]\(\boxed{8x^2 + 6x + 36xy^2 + 27y^2}\)[/tex].
1. Distribute each term in the first expression to every term in the second expression. This involves multiplying each term in [tex]\((-2x - 9y^2)\)[/tex] by each term in [tex]\((-4x - 3)\)[/tex].
2. Multiply the first term of the first expression with each term of the second expression:
- Multiply [tex]\(-2x\)[/tex] with [tex]\(-4x\)[/tex]:
[tex]\[
(-2x) \times (-4x) = 8x^2
\][/tex]
- Multiply [tex]\(-2x\)[/tex] with [tex]\(-3\)[/tex]:
[tex]\[
(-2x) \times (-3) = 6x
\][/tex]
3. Multiply the second term of the first expression with each term of the second expression:
- Multiply [tex]\(-9y^2\)[/tex] with [tex]\(-4x\)[/tex]:
[tex]\[
(-9y^2) \times (-4x) = 36xy^2
\][/tex]
- Multiply [tex]\(-9y^2\)[/tex] with [tex]\(-3\)[/tex]:
[tex]\[
(-9y^2) \times (-3) = 27y^2
\][/tex]
4. Combine all these results to get the expanded product:
[tex]\[
8x^2 + 6x + 36xy^2 + 27y^2
\][/tex]
So, the product of the expression [tex]\((-2x - 9y^2)(-4x - 3)\)[/tex] is [tex]\(\boxed{8x^2 + 6x + 36xy^2 + 27y^2}\)[/tex].
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