Answer :
The equivalent expression to [tex]\((2x + 3y^4)(-4x^2 + 9y^4)\) is \(-8x^3 - 12x^2y^4 + 18xy^4 + 27y^8\)[/tex], which is represented by option B.
Let's find the expression equivalent to [tex]\((2x + 3y^4)(-4x^2 + 9y^4)\)[/tex] by multiplying the two expressions using the distributive property:
[tex]\((2x + 3y^4)(-4x^2 + 9y^4) = 2x(-4x^2 + 9y^4) + 3y^4(-4x^2 + 9y^4)\)[/tex]
Now, let's perform the multiplication:
[tex]\(2x(-4x^2) + 2x(9y^4) + 3y^4(-4x^2) + 3y^4(9y^4)\)[/tex]
Simplify each term:
[tex]\(-8x^3 + 18xy^4 - 12x^2y^4 + 27y^8\)[/tex]
Now, let's combine like terms:
[tex]\(-8x^3 - 12x^2y^4 + 18xy^4 + 27y^8\)[/tex]
This is the expanded form of the expression, and none of the given options matches it exactly. However, if we reorganize the terms, we get:
[tex]\(-8x^3 - 12x^2y^4 + 18xy^4 + 27y^8\)[/tex]
So, the expression equivalent to [tex]\((2x + 3y^4)(-4x^2 + 9y^4)\)[/tex] is option B:
B. [tex]\(-8x^3 - 12x^2y^4 + 18xy^4 + 27y^8\)[/tex]
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