Find the Product (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 $- 1$ by $3$ .

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

Multiply $3$ by $- 1$ .

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

Multiply $- 1$ by $- 1$ .

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

Subtract $3 x$ from $- 3 x$ .

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