Question

How do you multiply: `(a-5)(a^2+5a+25)`?

Answer 1

• We know the identity
  `color(blue)(x^3 - y^3 = (x-y)(x^2+xy+y^2)`

The expression given to us is in the form `(x-y)(x^2+xy+y^2)` where:
`x = a, and y =5`

Hence the expression can directly be written as `a^3 - 5^3 = color(green)(a^3 - 125`

• But if we are not familiar with the identity we can use the Distributive Property of Multiplication to solve this expression

`(a-5)(a^2+5a+25)`

`a*(a^2+5a+25) - 5(a^2+5a+25)`

`= (a*a^2) +(a*5a) +(a*25) - (5*a^2) - (5*5a) - (5*25)`

`= a^3 + cancel(5a^2) +cancel(25a) - cancel(5a^2) - cancel(25a) - 125`

`color(green)( = a^3 - 125`