Simplify a(1+2a)-a(4a-5)

$a (1 + 2 a) - a (4 a - 5)$

Simplify each term.

Apply the distributive property.

$a \cdot 1 + a (2 a) - a (4 a - 5)$

Multiply $a$ by $1$ .

$a + a (2 a) - a (4 a - 5)$

Rewrite using the commutative property of multiplication.

$a + 2 a \cdot a - a (4 a - 5)$

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

Move $a$ .

$a + 2 (a \cdot a) - a (4 a - 5)$

Multiply $a$ by $a$ .

$a + 2 a^{2} - a (4 a - 5)$

Apply the distributive property.

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

Rewrite using the commutative property of multiplication.

$a + 2 a^{2} - 1 \cdot 4 a \cdot a - a \cdot - 5$

Multiply $- 5$ by $- 1$ .

$a + 2 a^{2} - 1 \cdot 4 a \cdot a + 5 a$

Simplify each term.

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

Move $a$ .

$a + 2 a^{2} - 1 \cdot 4 (a \cdot a) + 5 a$

Multiply $a$ by $a$ .

$a + 2 a^{2} - 1 \cdot 4 a^{2} + 5 a$

Multiply $- 1$ by $4$ .

$a + 2 a^{2} - 4 a^{2} + 5 a$

Simplify by adding terms.

Add $a$ and $5 a$ .

$2 a^{2} - 4 a^{2} + 6 a$

Subtract $4 a^{2}$ from $2 a^{2}$ .

$- 2 a^{2} + 6 a$