Question

Multiply (x-1)(x³+4x²+4x-1) and combine like terms. Explain how you reached your answer.

Answer 1

x⁴+3x³ -5x +1

Explanation:

To multiply this we are going to multiply each term of the binomial by each term of the polynomial.

`(x-1)(x^(3)+4x^(2)  +4x-1)\\=x^4+4x^3+4x^2-x -x^3-4x^2-4x+1`

Now we are going to combine like terms (this means we are going to sum up terms with the same exponent)

`x^4+4x^3+4x^2-x -x^3-4x^2-4x+1 = x^4 +(4x^3-x^3)+(4x^2-4x^2)+(-x-4x)+1\\=x^4+3x^3-5x+1`

Thus, the answer is x⁴+3x³ -5x +1