Simplify (3x-5)^2

${(3 x - 5)}^{2}$

Step 1

Rewrite ${(3 x - 5)}^{2}$ as $(3 x - 5) (3 x - 5)$ .

$(3 x - 5) (3 x - 5)$

Step 2

Expand $(3 x - 5) (3 x - 5)$ using the FOIL Method.

Apply the distributive property.

$3 x (3 x - 5) - 5 (3 x - 5)$

Apply the distributive property.

$3 x (3 x) + 3 x \cdot - 5 - 5 (3 x - 5)$

Apply the distributive property.

$3 x (3 x) + 3 x \cdot - 5 - 5 (3 x) - 5 \cdot - 5$

Step 3

Simplify and combine like terms.

Simplify each term.

Rewrite using the commutative property of multiplication.

$3 \cdot 3 x \cdot x + 3 x \cdot - 5 - 5 (3 x) - 5 \cdot - 5$

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

Move $x$ .

$3 \cdot 3 (x \cdot x) + 3 x \cdot - 5 - 5 (3 x) - 5 \cdot - 5$

Multiply $x$ by $x$ .

$3 \cdot 3 x^{2} + 3 x \cdot - 5 - 5 (3 x) - 5 \cdot - 5$

Multiply $3$ by $3$ .

$9 x^{2} + 3 x \cdot - 5 - 5 (3 x) - 5 \cdot - 5$

Multiply $- 5$ by $3$ .

$9 x^{2} - 15 x - 5 (3 x) - 5 \cdot - 5$

Multiply $3$ by $- 5$ .

$9 x^{2} - 15 x - 15 x - 5 \cdot - 5$

Multiply $- 5$ by $- 5$ .

$9 x^{2} - 15 x - 15 x + 25$

Subtract $15 x$ from $- 15 x$ .

$9 x^{2} - 30 x + 25$