Simplify (5x-1)(5x-1)

$(5 x - 1) (5 x - 1)$

Step 1

Expand $(5 x - 1) (5 x - 1)$ using the FOIL Method.

Apply the distributive property.

$5 x (5 x - 1) - 1 (5 x - 1)$

Apply the distributive property.

$5 x (5 x) + 5 x \cdot - 1 - 1 (5 x - 1)$

Apply the distributive property.

$5 x (5 x) + 5 x \cdot - 1 - 1 (5 x) - 1 \cdot - 1$

Step 2

Simplify and combine like terms.

Simplify each term.

Rewrite using the commutative property of multiplication.

$5 \cdot 5 x \cdot x + 5 x \cdot - 1 - 1 (5 x) - 1 \cdot - 1$

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

Move $x$ .

$5 \cdot 5 (x \cdot x) + 5 x \cdot - 1 - 1 (5 x) - 1 \cdot - 1$

Multiply $x$ by $x$ .

$5 \cdot 5 x^{2} + 5 x \cdot - 1 - 1 (5 x) - 1 \cdot - 1$

Multiply $5$ by $5$ .

$25 x^{2} + 5 x \cdot - 1 - 1 (5 x) - 1 \cdot - 1$

Multiply $- 1$ by $5$ .

$25 x^{2} - 5 x - 1 (5 x) - 1 \cdot - 1$

Multiply $5$ by $- 1$ .

$25 x^{2} - 5 x - 5 x - 1 \cdot - 1$

Multiply $- 1$ by $- 1$ .

$25 x^{2} - 5 x - 5 x + 1$

Subtract $5 x$ from $- 5 x$ .

$25 x^{2} - 10 x + 1$