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

Let's expand:

{(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 b

+ b a

+ b \cdot b

a \cdot a

+ a b

+ b a

+ b \cdot b

ⓘ Multiplying powers with the same base adds the exponents:

a \cdot a

a^{2}

b \cdot b

b^{2}

■Like terms are grouped by adding their coefficients:

a b + b a

2 a b

▶Expanded form:

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