Simplify (5x-8)(2x-5)

$(5 x - 8) (2 x - 5)$

Step 1

Expand $(5 x - 8) (2 x - 5)$ using the FOIL Method.

Apply the distributive property.

$5 x (2 x - 5) - 8 (2 x - 5)$

Apply the distributive property.

$5 x (2 x) + 5 x \cdot - 5 - 8 (2 x - 5)$

Apply the distributive property.

$5 x (2 x) + 5 x \cdot - 5 - 8 (2 x) - 8 \cdot - 5$

Step 2

Simplify and combine like terms.

Simplify each term.

Rewrite using the commutative property of multiplication.

$5 \cdot 2 x \cdot x + 5 x \cdot - 5 - 8 (2 x) - 8 \cdot - 5$

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

Move $x$ .

$5 \cdot 2 (x \cdot x) + 5 x \cdot - 5 - 8 (2 x) - 8 \cdot - 5$

Multiply $x$ by $x$ .

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

Multiply $5$ by $2$ .

$10 x^{2} + 5 x \cdot - 5 - 8 (2 x) - 8 \cdot - 5$

Multiply $- 5$ by $5$ .

$10 x^{2} - 25 x - 8 (2 x) - 8 \cdot - 5$

Multiply $2$ by $- 8$ .

$10 x^{2} - 25 x - 16 x - 8 \cdot - 5$

Multiply $- 8$ by $- 5$ .

$10 x^{2} - 25 x - 16 x + 40$

Subtract $16 x$ from $- 25 x$ .

$10 x^{2} - 41 x + 40$