Answer :
To find the product of [tex]\((-2x - 9y^2)(-4x - 3)\)[/tex], let's expand the expression by using the distributive property, often referred to as the FOIL method (First, Outer, Inner, Last) for binomials.
1. First: Multiply the first terms of each binomial:
[tex]\((-2x) \times (-4x) = 8x^2\)[/tex].
2. Outer: Multiply the outer terms:
[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 of each binomial:
[tex]\((-9y^2) \times (-3) = 27y^2\)[/tex].
Now, combine all these results:
The expression becomes:
[tex]\[ 8x^2 + 6x + 36xy^2 + 27y^2 \][/tex]
Hence, the product of [tex]\((-2x - 9y^2)(-4x - 3)\)[/tex] is:
[tex]\[ 8x^2 + 36xy^2 + 6x + 27y^2 \][/tex]
This matches one of the given options:
[tex]\[ 8x^2 + 6x + 36xy^2 + 27y^2 \][/tex]
1. First: Multiply the first terms of each binomial:
[tex]\((-2x) \times (-4x) = 8x^2\)[/tex].
2. Outer: Multiply the outer terms:
[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 of each binomial:
[tex]\((-9y^2) \times (-3) = 27y^2\)[/tex].
Now, combine all these results:
The expression becomes:
[tex]\[ 8x^2 + 6x + 36xy^2 + 27y^2 \][/tex]
Hence, the product of [tex]\((-2x - 9y^2)(-4x - 3)\)[/tex] is:
[tex]\[ 8x^2 + 36xy^2 + 6x + 27y^2 \][/tex]
This matches one of the given options:
[tex]\[ 8x^2 + 6x + 36xy^2 + 27y^2 \][/tex]
