factoring (x-7)^3?

(x-a)^3 = x^3 - 3ax^2 +3a^2 x - a^3

The coefficients are 1, -3, 3, 1

Look up "binomial coefficients" or "binomial expansion" to see where the 1, -3, 3, 1 came from.

This lets you quickly expand (x +- a) to an arbitrary power.

Or, you could just multiply it out

(x-7)^2 = x^2 -14x + 49

[x^2 -14x + 49](x-7) and so forth

1)
(x - 7)^3
= (x - 7)(x - 7)(x - 7)
= (x^2 - 7x - 7x + 49)(x - 7)
= (x^2 - 14x + 49)(x - 7)
= x^3 -14x^4 + 49x - 7x^2 + 98x - 343
= x^3 - 21x^2 + 147x - 343

(x-y)^3=
x^3+y^3-3x^2y+xy^2