Question

Factor using sum and product:

Answer 1

`x^4 - 1 = (x- 1)(x + 1)(x^2 + 1)`

`2x^2 - 4x - 240 = 2(x + 10) (x - 12)`

Explanation:

Given

`1.\ x^4 - 1`

`2.\ 2x^2 - 4x - 240`

Required

Factor

`1.\ x^4 - 1`

Express as difference of two squares

`x^4 - 1 = (x^2 - 1)(x^2 + 1)`

Express
`x^2 - 1` as difference of two squares

`x^4 - 1 = (x- 1)(x + 1)(x^2 + 1)`

`2.\ 2x^2 - 4x - 240`

Expand

`2x^2 - 4x - 240 = 2x^2 -24x + 20x - 240`

Factorize

`2x^2 - 4x - 240 = 2x(x -12) + 20(x - 12)`

Factor out x - 12

`2x^2 - 4x - 240 = (2x + 20) (x - 12)`

Factor out 2

`2x^2 - 4x - 240 = 2(x + 10) (x - 12)`