Simplify (5x-4)^2

${(5 x - 4)}^{2}$

Step 1

Rewrite ${(5 x - 4)}^{2}$ as $(5 x - 4) (5 x - 4)$ .

$(5 x - 4) (5 x - 4)$

Step 2

Expand $(5 x - 4) (5 x - 4)$ using the FOIL Method.

Apply the distributive property.

$5 x (5 x - 4) - 4 (5 x - 4)$

Apply the distributive property.

$5 x (5 x) + 5 x \cdot - 4 - 4 (5 x - 4)$

Apply the distributive property.

$5 x (5 x) + 5 x \cdot - 4 - 4 (5 x) - 4 \cdot - 4$

Step 3

Simplify and combine like terms.

Simplify each term.

Rewrite using the commutative property of multiplication.

$5 \cdot 5 x \cdot x + 5 x \cdot - 4 - 4 (5 x) - 4 \cdot - 4$

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

Move $x$ .

$5 \cdot 5 (x \cdot x) + 5 x \cdot - 4 - 4 (5 x) - 4 \cdot - 4$

Multiply $x$ by $x$ .

$5 \cdot 5 x^{2} + 5 x \cdot - 4 - 4 (5 x) - 4 \cdot - 4$

Multiply $5$ by $5$ .

$25 x^{2} + 5 x \cdot - 4 - 4 (5 x) - 4 \cdot - 4$

Multiply $- 4$ by $5$ .

$25 x^{2} - 20 x - 4 (5 x) - 4 \cdot - 4$

Multiply $5$ by $- 4$ .

$25 x^{2} - 20 x - 20 x - 4 \cdot - 4$

Multiply $- 4$ by $- 4$ .

$25 x^{2} - 20 x - 20 x + 16$

Subtract $20 x$ from $- 20 x$ .

$25 x^{2} - 40 x + 16$