To simplify the expression 6cos(40°) - 8cos^3(40°), we need to apply the trigonometric identity for the cube of cosine:

cos^3(θ) = (cos(θ))^3 - 3cos(θ)sin^2(θ)

Given that θ=40°, we substitute into the formula:

cos^3(40°) = (cos(40°))^3 - 3cos(40°)sin^2(40°)

Then, we can rewrite the original expression as:

6cos(40°) - 8[(cos(40°))^3 - 3cos(40°)sin^2(40°)]

Expanding and simplifying further:

6cos(40°) - 8cos^3(40°) + 24cos(40°)sin^2(40°)

We can stop here as this is the simplified expression for 6cos(40°) - 8cos^3(40°).