Question

select the correct answer.

which expression is equivalent to this polynomial expression?
\\((2x^5 + 3y^4)(-4x^2 + 9y^4)\\)

\\(\bigcirc -8x^7 + 27y^8\\)
\\(\bigcirc -2x^{10} + 11x^5y^4 - x^2y^4 + 12y^{16}\\)
\\(\bigcirc -2x^7 + 11x^5y^4 - x^2y^4 + 12y^8\\)
\\(\bigcirc -8x^7 + 18x^5y^4 - 12x^2y^4 + 27y^8\\)

Explanation:

Expand the expression using the distributive property

$$ (2x^5 + 3y^4)(-4x^2 + 9y^4) = 2x^5(-4x^2) + 2x^5(9y^4) + 3y^4(-4x^2) + 3y^4(9y^4) $$

Multiply individual terms using exponent rules

$$
LATEXBLOCK0
$$

Combine terms into the final polynomial expression

$$ -8x^7 + 18x^5y^4 - 12x^2y^4 + 27y^8 $$

Answer:

• (A) \(-8x^7 + 27y^8\)
• (B) \(-2x^{10} + 11x^5y^4 - x^2y^4 + 12y^{16}\)
• (C) \(-2x^7 + 11x^5y^4 - x^2y^4 + 12y^8\)
• (D) \(-8x^7 + 18x^5y^4 - 12x^2y^4 + 27y^8\) (Correct answer)