Common factor

The reverse of the distributive property is to get the common factor.

a · b + a · c = a·(b + c); a · c + b · c = (a + b)· c

Examples:

a² + ab = a · a + a · b = a ·(a + b)

4x³ + 8x² - 2x = 2 · 2 · x · x · x + 2 · 2 · 2 · x · x - 2 · x = 2x ·(2x² + 4x - 1)

Exercise: get the common factor to these polynomials:

a) 3xy + 6xy² - 12x²y²

b) 16x³ + 12x² + 28x

c) 18abc + 12ab²c³ - 24abc⁵ - 6ac

Solutions: a) 3xy·(1 + 2y - 4xy); b) 4x·(4x² + 3x + 7); c) 6ac·(3b + 2b²c² - 4bc⁴ - 1)