Simplify (5x-2)^2

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

Step 1

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

$(5 x - 2) (5 x - 2)$

Step 2

Expand $(5 x - 2) (5 x - 2)$ using the FOIL Method.

Apply the distributive property.

$5 x (5 x - 2) - 2 (5 x - 2)$

Apply the distributive property.

$5 x (5 x) + 5 x \cdot - 2 - 2 (5 x - 2)$

Apply the distributive property.

$5 x (5 x) + 5 x \cdot - 2 - 2 (5 x) - 2 \cdot - 2$

Step 3

Simplify and combine like terms.

Simplify each term.

Rewrite using the commutative property of multiplication.

$5 \cdot 5 x \cdot x + 5 x \cdot - 2 - 2 (5 x) - 2 \cdot - 2$

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

Move $x$ .

$5 \cdot 5 (x \cdot x) + 5 x \cdot - 2 - 2 (5 x) - 2 \cdot - 2$

Multiply $x$ by $x$ .

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

Multiply $5$ by $5$ .

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

Multiply $- 2$ by $5$ .

$25 x^{2} - 10 x - 2 (5 x) - 2 \cdot - 2$

Multiply $5$ by $- 2$ .

$25 x^{2} - 10 x - 10 x - 2 \cdot - 2$

Multiply $- 2$ by $- 2$ .

$25 x^{2} - 10 x - 10 x + 4$

Subtract $10 x$ from $- 10 x$ .

$25 x^{2} - 20 x + 4$