Simplify (3x+1)^2

${(3 x + 1)}^{2}$

Step 1

Rewrite ${(3 x + 1)}^{2}$ as $(3 x + 1) (3 x + 1)$ .

$(3 x + 1) (3 x + 1)$

Step 2

Expand $(3 x + 1) (3 x + 1)$ using the FOIL Method.

Apply the distributive property.

$3 x (3 x + 1) + 1 (3 x + 1)$

Apply the distributive property.

$3 x (3 x) + 3 x \cdot 1 + 1 (3 x + 1)$

Apply the distributive property.

$3 x (3 x) + 3 x \cdot 1 + 1 (3 x) + 1 \cdot 1$

Step 3

Simplify and combine like terms.

Simplify each term.

Rewrite using the commutative property of multiplication.

$3 \cdot 3 x \cdot x + 3 x \cdot 1 + 1 (3 x) + 1 \cdot 1$

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

Move $x$ .

$3 \cdot 3 (x \cdot x) + 3 x \cdot 1 + 1 (3 x) + 1 \cdot 1$

Multiply $x$ by $x$ .

$3 \cdot 3 x^{2} + 3 x \cdot 1 + 1 (3 x) + 1 \cdot 1$

Multiply $3$ by $3$ .

$9 x^{2} + 3 x \cdot 1 + 1 (3 x) + 1 \cdot 1$

Multiply $3$ by $1$ .

$9 x^{2} + 3 x + 1 (3 x) + 1 \cdot 1$

Multiply $3 x$ by $1$ .

$9 x^{2} + 3 x + 3 x + 1 \cdot 1$

Multiply $1$ by $1$ .

$9 x^{2} + 3 x + 3 x + 1$

Add $3 x$ and $3 x$ .

$9 x^{2} + 6 x + 1$