expand (x-1)^2 — step-by-step solution

Let's expand:

{(x - 1)}^{2}

ⓘ Raising a sum to an integer power is multiplying it by itself:

{(x - 1)}^{2}

(x - 1) \cdot (x - 1)

(x - 1) \cdot (x - 1)

ⓘ Expand by multiplying each term inside the parentheses:

(x - 1) \cdot (x - 1)

x \cdot x

+ x \cdot (-1)

- 1 \cdot x

- 1 \cdot (-1)

x \cdot x

+ x \cdot (-1)

- 1 \cdot x

- 1 \cdot (-1)

ⓘ Multiplying powers with the same base adds the exponents:

x \cdot x

x^{2}

■Multiplying by -1 gives the opposite:

x \cdot (-1)

- x

■Multiplying by 1 changes nothing:

1 \cdot x

x

■Multiplications are done before additions and subtractions. Two minus signs cancel out, the product of two negative numbers is positive:

-1 \cdot (-1)

1

x^{2}

- x

- x

+ 1

ⓘ Like terms are grouped by adding their coefficients:

- x - x

-2 x

▶Expanded form:

x^{2} - 2 x + 1