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

Let's write in expanded form:

{(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}

■Multiplications are done before additions and subtractions:

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