Simplify -2a(b+3-2a)

$- 2 a (b + 3 - 2 a)$

Step 1

Apply the distributive property.

$- 2 a b - 2 a \cdot 3 - 2 a (- 2 a)$

Step 2

Simplify.

Multiply $3$ by $- 2$ .

$- 2 a b - 6 a - 2 a (- 2 a)$

Rewrite using the commutative property of multiplication.

$- 2 a b - 6 a - 2 \cdot - 2 a \cdot a$

Step 3

Simplify each term.

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

Move $a$ .

$- 2 a b - 6 a - 2 \cdot - 2 (a \cdot a)$

Multiply $a$ by $a$ .

$- 2 a b - 6 a - 2 \cdot - 2 a^{2}$

Multiply $- 2$ by $- 2$ .

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