Question

How to write function in standard form

`f(x) = (2 * + 1)(x + 1)(x - 1)`

Answer 1

The standard form:

`f(x)=ax^3+bx^2+cx+d`
Use:
`(a-b)(a+b)=a^2-b^2\\\\(a+b)(c+d)=ab+ad+bc+bd\\\\a^n\cdot a^m=a^(n+m)`

`f(x)=(2x+1)(x+1)(x-1)\\\\f(x)=(2x+1)(x^2-1^2)\\\\f(x)=(2x+1)(x^2-1)\\\\f(x)=2x\cdot x^2-2x\cdot1+1\cdotx^2-1\cdot1\\\\f(x)=2x^3-2x+x^2-1\\\\\boxed{f(x)=2x^3+x^2-2x-1}`

Answer 2

Multiply it out.
f(x) = (2x +1)(x² -1) . . . . . . recognize the factoring of the difference of squares
f(x) = 2x³ +x² -2x -1