Which expression is equivalent to this polynomial expression?

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

A. $2x^7 + 11x^3$
B. $x^3y^2 + 12y^3 - 8x^7 + 18x^3y^4 - 12x^2y + 27y^3$
C. $-8x^7 + 27y^3$
D. $2x^{10} + 11x^3y^4 x^2y + 12y^{16}$

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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Which expression is equivalent to this polynomial expression?\[(2x + 3y^4)(-4x^2 + 9y^4)\]A. \(2x^7 + 11x^3\)B. \(x^3y^2 + 12y^3 - 8x^7 + 18x^3y^4 - 12x^2y + 27y^3\)C. \(-8x^7 + 27y^3\)D. \(2x^{10} + 11x^3y^4 x^2y + 12y^{16}\)

Answer :

Other Questions

Which expression is equivalent to this polynomial expression?

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

A. \(2x^7 + 11x^3\)
B. \(x^3y^2 + 12y^3 - 8x^7 + 18x^3y^4 - 12x^2y + 27y^3\)
C. \(-8x^7 + 27y^3\)
D. \(2x^{10} + 11x^3y^4 x^2y + 12y^{16}\)