Answer :
Let's find the product of the expression [tex]\((-2x - 9y^2)(-4x - 3)\)[/tex].
To solve this, we'll use the distributive property, also known as the FOIL method in the context of multiplying binomials:
1. First: Multiply the first terms from each binomial.
[tex]\[
(-2x) \cdot (-4x) = 8x^2
\][/tex]
2. Outer: Multiply the outer terms in the expression.
[tex]\[
(-2x) \cdot (-3) = 6x
\][/tex]
3. Inner: Multiply the inner terms of the expression.
[tex]\[
(-9y^2) \cdot (-4x) = 36xy^2
\][/tex]
4. Last: Multiply the last terms of each binomial.
[tex]\[
(-9y^2) \cdot (-3) = 27y^2
\][/tex]
Now, add all these results together to get the final expression:
[tex]\[
8x^2 + 6x + 36xy^2 + 27y^2
\][/tex]
So, the product of the given expression is:
[tex]\[
8x^2 + 6x + 36xy^2 + 27y^2
\][/tex]
To solve this, we'll use the distributive property, also known as the FOIL method in the context of multiplying binomials:
1. First: Multiply the first terms from each binomial.
[tex]\[
(-2x) \cdot (-4x) = 8x^2
\][/tex]
2. Outer: Multiply the outer terms in the expression.
[tex]\[
(-2x) \cdot (-3) = 6x
\][/tex]
3. Inner: Multiply the inner terms of the expression.
[tex]\[
(-9y^2) \cdot (-4x) = 36xy^2
\][/tex]
4. Last: Multiply the last terms of each binomial.
[tex]\[
(-9y^2) \cdot (-3) = 27y^2
\][/tex]
Now, add all these results together to get the final expression:
[tex]\[
8x^2 + 6x + 36xy^2 + 27y^2
\][/tex]
So, the product of the given expression is:
[tex]\[
8x^2 + 6x + 36xy^2 + 27y^2
\][/tex]
