Question

What is the linear factor of the expression 27x3−64y3?.(1 point)%0D%0AResponses%0D%0A%0D%0A3x+4y%0D%0A3 x plus 4 y%0D%0A%0D%0A27x−64y%0D%0A27 x minus 64 y%0D%0A%0D%0A3x−4y%0D%0A3 x minus 4 y%0D%0A%0D%0Ax−y

Answer 1

To factor the expression \( 27x^3 - 64y^3 \), we recognize that it is a difference of cubes. The difference of cubes can be factored using the formula:

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

In this case, we have:

- \( a = 3x \) (since \( (3x)^3 = 27x^3 \))
- \( b = 4y \) (since \( (4y)^3 = 64y^3 \))

Applying the formula:

1. First, we calculate \( a - b \):
\[
3x - 4y
\]

2. Next, we find \( a^2 + ab + b^2 \):
- \( a^2 = (3x)^2 = 9x^2 \)
- \( ab = (3x)(4y) = 12xy \)
- \( b^2 = (4y)^2 = 16y^2 \)

So,
\[
a^2 + ab + b^2 = 9x^2 + 12xy + 16y^2
\]

Thus, the factored form of \( 27x^3 - 64y^3 \) is:

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

The linear factor of the expression is therefore:

\[
3x - 4y
\]

So the response is:

**3 x minus 4 y**.