Simplify (4x+2)^2

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

Step 1

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

$(4 x + 2) (4 x + 2)$

Step 2

Expand $(4 x + 2) (4 x + 2)$ using the FOIL Method.

Apply the distributive property.

$4 x (4 x + 2) + 2 (4 x + 2)$

Apply the distributive property.

$4 x (4 x) + 4 x \cdot 2 + 2 (4 x + 2)$

Apply the distributive property.

$4 x (4 x) + 4 x \cdot 2 + 2 (4 x) + 2 \cdot 2$

Step 3

Simplify and combine like terms.

Simplify each term.

Rewrite using the commutative property of multiplication.

$4 \cdot 4 x \cdot x + 4 x \cdot 2 + 2 (4 x) + 2 \cdot 2$

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

Move $x$ .

$4 \cdot 4 (x \cdot x) + 4 x \cdot 2 + 2 (4 x) + 2 \cdot 2$

Multiply $x$ by $x$ .

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

Multiply $4$ by $4$ .

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

Multiply $2$ by $4$ .

$16 x^{2} + 8 x + 2 (4 x) + 2 \cdot 2$

Multiply $4$ by $2$ .

$16 x^{2} + 8 x + 8 x + 2 \cdot 2$

Multiply $2$ by $2$ .

$16 x^{2} + 8 x + 8 x + 4$

Add $8 x$ and $8 x$ .

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