Question

Select the expression that is equivalent to (x - 1)2.

O A. x2 - 2x + 2
O B. x2 - x + 2
O C. x2 - x + 1
O D. x2 – 2x + 1

Answer 1

`\boxed{\sf D. \ {x}^(2) - 2x + 1}`

Explanation:

`\sf Expand \: the \: following: \\ \sf \implies {(x - 1)}^(2) \\ \\ \sf \implies (x - 1)(x - 1) \\ \\ \sf \implies x(x - 1) - 1(x - 1) \\ \\ \sf \implies (x)(x) - (1)(x) - (1)(x) - (1)( - 1) \\ \\ \sf \implies {x}^(2) - x - x - ( - 1) \\ \\ \sf \implies {x}^(2) - 2x - ( - 1) \\ \\ \sf \implies {x}^(2) - 2x + 1`

Answer 2

x^2 -2x+1

Explanation:

(x - 1)^2

(x-1) * (x-1)

FOIL

first: x^2

outer: -1x

inner: -1x

last: 1

Add together

x^2 -1x-1x+1

Combine like terms

x^2 -2x+1