Get detailed and reliable answers to your questions on IDNLearn.com. Discover comprehensive answers to your questions from our community of knowledgeable experts.

Select the correct answer.

Which expression is equivalent to the following polynomial expression?
[tex]\[ \left(2 x^5 + 3 y^4\right)\left(-4 x^2 + 9 y^4\right) \][/tex]

A. [tex]\(-8 x^7 + 18 x^5 y^4 - 12 x^2 y^4 + 27 y^8\)[/tex]

B. [tex]\(-8 x^7 + 27 y^8\)[/tex]

C. [tex]\(-2 x^7 + 11 x^5 y^4 - x^2 y^4 + 12 y^8\)[/tex]

D. [tex]\(-2 x^{10} + 11 x^5 y^4 - x^2 y^4 + 12 y^{16}\)[/tex]


Sagot :

To solve the problem, we begin by using the distributive property (also known as the FOIL method for binomials) to expand the given polynomial expression:

[tex]\[ (2x^5 + 3y^4)(-4x^2 + 9y^4) \][/tex]

Let's distribute each term in the first parenthesis to each term in the second parenthesis:

1. Multiply [tex]\(2x^5\)[/tex] by [tex]\(-4x^2\)[/tex]:
[tex]\[ 2x^5 \cdot (-4x^2) = -8x^{5+2} = -8x^7 \][/tex]

2. Multiply [tex]\(2x^5\)[/tex] by [tex]\(9y^4\)[/tex]:
[tex]\[ 2x^5 \cdot 9y^4 = 18x^5y^4 \][/tex]

3. Multiply [tex]\(3y^4\)[/tex] by [tex]\(-4x^2\)[/tex]:
[tex]\[ 3y^4 \cdot (-4x^2) = -12x^2y^4 \][/tex]

4. Multiply [tex]\(3y^4\)[/tex] by [tex]\(9y^4\)[/tex]:
[tex]\[ 3y^4 \cdot 9y^4 = 27y^{4+4} = 27y^8 \][/tex]

Now, let's combine the results from all multiplications:
[tex]\[ -8x^7 + 18x^5y^4 - 12x^2y^4 + 27y^8 \][/tex]

Therefore, the expression equivalent to [tex]\((2x^5 + 3y^4)(-4x^2 + 9y^4)\)[/tex] is:

[tex]\[ \boxed{-8x^7 + 18x^5y^4 - 12x^2y^4 + 27y^8} \][/tex]

Thus, the correct answer is:
A. [tex]\(-8x^7 + 18x^5y^4 - 12x^2y^4 + 27y^8\)[/tex]