Question

select the correct answer.

which expression is equivalent to the given polynomial expression?
\\((g - h)(g^2 - 3gh + 2h^2)\\)

\\(\bigcirc g^3 - 4g^2h + 5gh^2 - 2h^3\\)
\\(\bigcirc g^3 - 2h^3\\)
\\(\bigcirc g^3 - 2g^2h + gh^2 - 2h^3\\)
\\(\bigcirc g^3 + 4g^2h^2 - 2h^3\\)

Explanation:

Expand the polynomial expression

$$ (g - h)(g^2 - 3gh + 2h^2) = g(g^2 - 3gh + 2h^2) - h(g^2 - 3gh + 2h^2) $$

$$ = g^3 - 3g^2h + 2gh^2 - g^2h + 3gh^2 - 2h^3 $$

Combine like terms

$$ g^3 + (-3g^2h - g^2h) + (2gh^2 + 3gh^2) - 2h^3 $$

$$ = g^3 - 4g^2h + 5gh^2 - 2h^3 $$

Answer:

• (A) \(g^3 - 4g^2h + 5gh^2 - 2h^3\) (Correct answer)
• (B) \(g^3 - 2h^3\)
• (C) \(g^3 - 2g^2h + gh^2 - 2h^3\)
• (D) \(g^3 + 4g^2h^2 - 2h^3\)