Answer :
To find the product [tex]\((-2x - 9y^2)(-4x - 3)\)[/tex], we can use the distributive property, often called the FOIL method in this context, which stands for First, Outer, Inner, and Last. Let's break it down step-by-step:
1. First Terms: Multiply the first terms from each binomial:
[tex]\((-2x) \times (-4x) = 8x^2\)[/tex].
2. Outer Terms: Multiply the outer terms from the binomials:
[tex]\((-2x) \times (-3) = 6x\)[/tex].
3. Inner Terms: Multiply the inner terms from the binomials:
[tex]\((-9y^2) \times (-4x) = 36xy^2\)[/tex].
4. Last Terms: Multiply the last terms from each binomial:
[tex]\((-9y^2) \times (-3) = 27y^2\)[/tex].
Now, combine all these terms to get the final expression:
[tex]\[8x^2 + 6x + 36xy^2 + 27y^2.\][/tex]
This is the product of the expression [tex]\((-2x - 9y^2)(-4x - 3)\)[/tex].
1. First Terms: Multiply the first terms from each binomial:
[tex]\((-2x) \times (-4x) = 8x^2\)[/tex].
2. Outer Terms: Multiply the outer terms from the binomials:
[tex]\((-2x) \times (-3) = 6x\)[/tex].
3. Inner Terms: Multiply the inner terms from the binomials:
[tex]\((-9y^2) \times (-4x) = 36xy^2\)[/tex].
4. Last Terms: Multiply the last terms from each binomial:
[tex]\((-9y^2) \times (-3) = 27y^2\)[/tex].
Now, combine all these terms to get the final expression:
[tex]\[8x^2 + 6x + 36xy^2 + 27y^2.\][/tex]
This is the product of the expression [tex]\((-2x - 9y^2)(-4x - 3)\)[/tex].
