Question

select the correct answer.

which expression is equivalent to this polynomial expression?
\\((2x^2 - 3y^2)(4x^4 + 6x^2y^2 + 9y^4)\\)

\\(6x^8 + 9x^4y^2 + 14x^2y^4 + 6y^8\\)
\\(8x^6 - 27y^6\\)
\\(8x^6 + 24x^4y^2 + 36x^2y^4 - 27y^6\\)
\\(8x^6 + 12x^4y^2 + 18x^2y^4\\)

Explanation:

Identify the algebraic pattern

$$ (a - b)(a^2 + ab + b^2) = a^3 - b^3 $$

Define the terms for substitution

$$
LATEXBLOCK0
$$

Apply the difference of cubes formula

$$
LATEXBLOCK1
$$

Answer:

• (A) \(6x^8 + 9x^4y^2 + 14x^2y^4 + 6y^8\)
• (B) \(8x^6 - 27y^6\) (Correct answer)
• (C) \(8x^6 + 24x^4y^2 + 36x^2y^4 - 27y^6\)
• (D) \(8x^6 + 12x^4y^2 + 18x^2y^4\)