`(a + b)^0 = 1`
`(a + b)^1 = a + b`
`(a + b)^ 2 = a^2 + 2ab + b^2`
`(a-b)^ 2 = a^2-2ab + b^2`
`(a + b)^ 3 = a^3 + 3a^2 b + 3ab^2 + b^3`
`(a-b)^ 3 = a^3 -3a^2 b + 3ab^2-b^3`
`(a + b)^4 = a^4 + 4a^3 b + 6a^2 b^2 + 4ab^3 + b^4`
And so on. These formulas are easy to remember because of their symmetry and these are used very frequently in Algebra. We will cover a number of examples that involve these formulas.
`x^2-y^2 = (x + y)(x-y)`
This formula indicates that we can determine the difference of two squares simply my taking a product of the sum and the difference of the variables involved.
`x^3 + y^3 = ( x + y ) ( x^2-xy + y^2 )`
`x^3-y^3 = ( x-y ) ( x^2 + xy + y^2 )`