Simplify (4x+1)^2

${(4 x + 1)}^{2}$

Step 1

Rewrite ${(4 x + 1)}^{2}$ as $(4 x + 1) (4 x + 1)$ .

$(4 x + 1) (4 x + 1)$

Step 2

Expand $(4 x + 1) (4 x + 1)$ using the FOIL Method.

Apply the distributive property.

$4 x (4 x + 1) + 1 (4 x + 1)$

Apply the distributive property.

$4 x (4 x) + 4 x \cdot 1 + 1 (4 x + 1)$

Apply the distributive property.

$4 x (4 x) + 4 x \cdot 1 + 1 (4 x) + 1 \cdot 1$

Step 3

Simplify and combine like terms.

Simplify each term.

Rewrite using the commutative property of multiplication.

$4 \cdot 4 x \cdot x + 4 x \cdot 1 + 1 (4 x) + 1 \cdot 1$

Multiply $x$ by $x$ by adding the exponents.

Move $x$ .

$4 \cdot 4 (x \cdot x) + 4 x \cdot 1 + 1 (4 x) + 1 \cdot 1$

Multiply $x$ by $x$ .

$4 \cdot 4 x^{2} + 4 x \cdot 1 + 1 (4 x) + 1 \cdot 1$

Multiply $4$ by $4$ .

$16 x^{2} + 4 x \cdot 1 + 1 (4 x) + 1 \cdot 1$

Multiply $4$ by $1$ .

$16 x^{2} + 4 x + 1 (4 x) + 1 \cdot 1$

Multiply $4 x$ by $1$ .

$16 x^{2} + 4 x + 4 x + 1 \cdot 1$

Multiply $1$ by $1$ .

$16 x^{2} + 4 x + 4 x + 1$

Add $4 x$ and $4 x$ .

$16 x^{2} + 8 x + 1$