Simplify (4x-5)^2

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

Step 1

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

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

Step 2

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

Apply the distributive property.

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

Apply the distributive property.

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

Apply the distributive property.

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

Step 3

Simplify and combine like terms.

Simplify each term.

Rewrite using the commutative property of multiplication.

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

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

Move $x$ .

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

Multiply $x$ by $x$ .

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

Multiply $4$ by $4$ .

$16 x^{2} + 4 x \cdot - 5 - 5 (4 x) - 5 \cdot - 5$

Multiply $- 5$ by $4$ .

$16 x^{2} - 20 x - 5 (4 x) - 5 \cdot - 5$

Multiply $4$ by $- 5$ .

$16 x^{2} - 20 x - 20 x - 5 \cdot - 5$

Multiply $- 5$ by $- 5$ .

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

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

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