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

Let's expand:

{(2 x + 1)}^{2}

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

{(2 x + 1)}^{2}

(2 x + 1) \cdot (2 x + 1)

(2 x + 1) \cdot (2 x + 1)

ⓘ Expand by multiplying each term inside the parentheses:

(2 x + 1) \cdot (2 x + 1)

2 \cdot x \cdot 2 \cdot x

+ 2 x \cdot 1

+ 1 \cdot 2 x

+ 1 \cdot 1

2 \cdot x \cdot 2 \cdot x

+ 2 x \cdot 1

+ 1 \cdot 2 x

+ 1 \cdot 1

ⓘ Multiplications are done before additions and subtractions:

2 \cdot 2

4

1 \cdot 1

1

■Multiplying powers with the same base adds the exponents:

x \cdot x

x^{2}

4 x^{2}

+ 2 x

+ 2 x

+ 1

ⓘ Like terms are grouped by adding their coefficients:

2 x + 2 x

4 x

▶Expanded form:

4 x^{2} + 4 x + 1