Simplify (8x-5)^2

${(8 x - 5)}^{2}$

Step 1

Rewrite ${(8 x - 5)}^{2}$ as $(8 x - 5) (8 x - 5)$ .

$(8 x - 5) (8 x - 5)$

Step 2

Expand $(8 x - 5) (8 x - 5)$ using the FOIL Method.

Apply the distributive property.

$8 x (8 x - 5) - 5 (8 x - 5)$

Apply the distributive property.

$8 x (8 x) + 8 x \cdot - 5 - 5 (8 x - 5)$

Apply the distributive property.

$8 x (8 x) + 8 x \cdot - 5 - 5 (8 x) - 5 \cdot - 5$

Step 3

Simplify and combine like terms.

Simplify each term.

Rewrite using the commutative property of multiplication.

$8 \cdot 8 x \cdot x + 8 x \cdot - 5 - 5 (8 x) - 5 \cdot - 5$

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

Move $x$ .

$8 \cdot 8 (x \cdot x) + 8 x \cdot - 5 - 5 (8 x) - 5 \cdot - 5$

Multiply $x$ by $x$ .

$8 \cdot 8 x^{2} + 8 x \cdot - 5 - 5 (8 x) - 5 \cdot - 5$

Multiply $8$ by $8$ .

$64 x^{2} + 8 x \cdot - 5 - 5 (8 x) - 5 \cdot - 5$

Multiply $- 5$ by $8$ .

$64 x^{2} - 40 x - 5 (8 x) - 5 \cdot - 5$

Multiply $8$ by $- 5$ .

$64 x^{2} - 40 x - 40 x - 5 \cdot - 5$

Multiply $- 5$ by $- 5$ .

$64 x^{2} - 40 x - 40 x + 25$

Subtract $40 x$ from $- 40 x$ .

$64 x^{2} - 80 x + 25$