Simplify (2a-1)(8a-5)

$(2 a - 1) (8 a - 5)$

Step 1

Expand $(2 a - 1) (8 a - 5)$ using the FOIL Method.

Apply the distributive property.

$2 a (8 a - 5) - 1 (8 a - 5)$

Apply the distributive property.

$2 a (8 a) + 2 a \cdot - 5 - 1 (8 a - 5)$

Apply the distributive property.

$2 a (8 a) + 2 a \cdot - 5 - 1 (8 a) - 1 \cdot - 5$

Step 2

Simplify and combine like terms.

Simplify each term.

Rewrite using the commutative property of multiplication.

$2 \cdot 8 a \cdot a + 2 a \cdot - 5 - 1 (8 a) - 1 \cdot - 5$

Multiply $a$ by $a$ by adding the exponents.

Move $a$ .

$2 \cdot 8 (a \cdot a) + 2 a \cdot - 5 - 1 (8 a) - 1 \cdot - 5$

Multiply $a$ by $a$ .

$2 \cdot 8 a^{2} + 2 a \cdot - 5 - 1 (8 a) - 1 \cdot - 5$

Multiply $2$ by $8$ .

$16 a^{2} + 2 a \cdot - 5 - 1 (8 a) - 1 \cdot - 5$

Multiply $- 5$ by $2$ .

$16 a^{2} - 10 a - 1 (8 a) - 1 \cdot - 5$

Multiply $8$ by $- 1$ .

$16 a^{2} - 10 a - 8 a - 1 \cdot - 5$

Multiply $- 1$ by $- 5$ .

$16 a^{2} - 10 a - 8 a + 5$

Subtract $8 a$ from $- 10 a$ .

$16 a^{2} - 18 a + 5$