Answer :
Sure! Let's solve the expression [tex]\((-2x - 9y^2)(-4x - 3)\)[/tex] step-by-step by distributing the terms.
1. Apply the distributive property: Distribute each term in the first set of parentheses to each term in the second set of parentheses.
[tex]\[
(-2x - 9y^2)(-4x - 3) = (-2x)(-4x) + (-2x)(-3) + (-9y^2)(-4x) + (-9y^2)(-3)
\][/tex]
2. Multiply each term:
- Multiply [tex]\((-2x)(-4x)\)[/tex]:
[tex]\[
(-2x)(-4x) = 8x^2
\][/tex]
- Multiply [tex]\((-2x)(-3)\)[/tex]:
[tex]\[
(-2x)(-3) = 6x
\][/tex]
- Multiply [tex]\((-9y^2)(-4x)\)[/tex]:
[tex]\[
(-9y^2)(-4x) = 36xy^2
\][/tex]
- Multiply [tex]\((-9y^2)(-3)\)[/tex]:
[tex]\[
(-9y^2)(-3) = 27y^2
\][/tex]
3. Combine all the results:
Adding these results together, we have:
[tex]\[
8x^2 + 6x + 36xy^2 + 27y^2
\][/tex]
So, the simplified result of the expression is:
[tex]\[ 8x^2 + 6x + 36xy^2 + 27y^2 \][/tex]
This is the expanded and simplified form of the original expression given.
1. Apply the distributive property: Distribute each term in the first set of parentheses to each term in the second set of parentheses.
[tex]\[
(-2x - 9y^2)(-4x - 3) = (-2x)(-4x) + (-2x)(-3) + (-9y^2)(-4x) + (-9y^2)(-3)
\][/tex]
2. Multiply each term:
- Multiply [tex]\((-2x)(-4x)\)[/tex]:
[tex]\[
(-2x)(-4x) = 8x^2
\][/tex]
- Multiply [tex]\((-2x)(-3)\)[/tex]:
[tex]\[
(-2x)(-3) = 6x
\][/tex]
- Multiply [tex]\((-9y^2)(-4x)\)[/tex]:
[tex]\[
(-9y^2)(-4x) = 36xy^2
\][/tex]
- Multiply [tex]\((-9y^2)(-3)\)[/tex]:
[tex]\[
(-9y^2)(-3) = 27y^2
\][/tex]
3. Combine all the results:
Adding these results together, we have:
[tex]\[
8x^2 + 6x + 36xy^2 + 27y^2
\][/tex]
So, the simplified result of the expression is:
[tex]\[ 8x^2 + 6x + 36xy^2 + 27y^2 \][/tex]
This is the expanded and simplified form of the original expression given.
