factor r^2-(b-c)^2

Question

I need to factor r^2-(b-c)^2

Answer 1

This is what is known as the difference of squares.  Any time you have a squared term minus another squared term, the factors are the square root of the first minus the square root of the second and the square root of the first plus the square root of the second: a² - b² = (a - b)(a + b)

r² -(b - c)²

[r - (b - c)][r + (b - c)]

(r -b + c)(r + b - c)