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 in these polynomials:

a) 2x⁷ - 36x⁵ + 12x² + 16x =

b) 3ab² + 12ab³ - 6a²b⁵ =

c) 12x²y⁵ - 6x²y² =

Solutions: a)  2x·(x⁵ - 18x⁴ + 6x + 8); b) 3ab²·(1 + 4b - 2ab³); c) 6x²y²·(2y³ - 1)