What is the linear factor of the expression 27x3−64y3 ?.(1 point) Responses x−y x minus y 27x−64y 27 x minus 64 y 3x+4y 3 x plus 4 y 3x−4y

Answer 1

The expression \( 27x^3 - 64y^3 \) represents a difference of cubes, which can be factored using the formula:

\[ a^3 - b^3 = (a - b)(a^2 + ab + b^2) \]

In this case, we can identify \( a = 3x \) (since \( (3x)^3 = 27x^3 \)) and \( b = 4y \) (since \( (4y)^3 = 64y^3 \)). Applying the difference of cubes formula:

1. \( a - b = 3x - 4y \)
2. \( a^2 = (3x)^2 = 9x^2 \)
3. \( ab = (3x)(4y) = 12xy \)
4. \( b^2 = (4y)^2 = 16y^2 \)

Thus, the full factorization is:

\[ 27x^3 - 64y^3 = (3x - 4y)(9x^2 + 12xy + 16y^2) \]

The linear factor of the expression \( 27x^3 - 64y^3 \) is \( 3x - 4y \).

So the correct response from the options you provided is:

3x - 4y