expand (a-b)^2 — step-by-step solution

Let's write in expanded form:

{(a - b)}^{2}

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

{(a - b)}^{2}

(a - b) \cdot (a - b)

(a - b) \cdot (a - b)

ⓘ Expand by multiplying each term inside the parentheses:

(a - b) \cdot (a - b)

a \cdot a

+ a \cdot (- b)

- b \cdot a

- b \cdot (- b)

a \cdot a

+ a \cdot (- b)

- b \cdot a

- b \cdot (- b)

ⓘ Multiplying powers with the same base adds the exponents:

a \cdot a

a^{2}

- b \cdot (- b)

{(- b)}^{2}

■The minus sign is placed in front of the product:

a \cdot (- b)

- a b

a^{2}

- a b

- b a

+ {(- b)}^{2}

ⓘ Like terms are grouped by adding their coefficients:

- a b - b a

-2 a b

■Powers are computed before multiplications, additions and subtractions. With an even integer exponent, the minus sign in the base disappears; with an odd integer exponent, it moves in front of the power:

{(- b)}^{2}

b^{2}

▶Expanded form:

a^{2} - 2 a b + b^{2}