To simplify the given expression, we can use the trigonometric identity:

sin^2(x) + cos^2(x) = 1

Recall that sin(2x) = 2sin(x)cos(x), we can rewrite the given expression as:

7sin^2(x) - 8sin(x)cos(x) - 7cos^2(x) = 7(sin^2(x) + cos^2(x)) - 8sin(x)cos(x)

Using the trigonometric identity sin^2(x) + cos^2(x) = 1:

7(1) - 8sin(x)cos(x) = 7 - 8sin(x)cos(x)

Therefore, the simplified expression is:

7 - 8sin(x)cos(x)