Show your work:

Use the distributive property in two different ways to find the product of 127 and 32.

The distributive property: a (b + c) = ab + ac

127 * 32 = 127 * (30 + 2) = 127 * 30 + 127 * 2 = (130 - 3) * 30 + (130 - 3) * 2

= (130) (30) - (3) (30) + (130) (2) - (3) (2) = 3900 - 90 + 260 - 6

= 3810 + 254 = 4064

127 * 32 = (130 - 3) * 32 = 130 * 32 - 3 * 32 = 130 * (30 + 2) - 96

= (130) (30) + (130) (2) - 96 = 3900 + 260 - (100 - 4) = 4160 - 100 + 4

= 4060 + 4 = 4064