Simplify (5x-3)^2

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

Step 1

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

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

Step 2

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

Apply the distributive property.

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

Apply the distributive property.

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

Apply the distributive property.

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

Step 3

Simplify and combine like terms.

Simplify each term.

Rewrite using the commutative property of multiplication.

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

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

Move $x$ .

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

Multiply $x$ by $x$ .

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

Multiply $5$ by $5$ .

$25 x^{2} + 5 x \cdot - 3 - 3 (5 x) - 3 \cdot - 3$

Multiply $- 3$ by $5$ .

$25 x^{2} - 15 x - 3 (5 x) - 3 \cdot - 3$

Multiply $5$ by $- 3$ .

$25 x^{2} - 15 x - 15 x - 3 \cdot - 3$

Multiply $- 3$ by $- 3$ .

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

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

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