Simplify b(a+b)-a(a-b)

$b (a + b) - a (a - b)$

Simplify each term.

Apply the distributive property.

$b a + b \cdot b - a (a - b)$

Multiply $b$ by $b$ .

$b a + b^{2} - a (a - b)$

Apply the distributive property.

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

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

Move $a$ .

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

Multiply $a$ by $a$ .

$b a + b^{2} - a^{2} - a (- b)$

Rewrite using the commutative property of multiplication.

$b a + b^{2} - a^{2} - 1 \cdot - 1 a b$

Simplify each term.

Multiply $- 1$ by $- 1$ .

$b a + b^{2} - a^{2} + 1 a b$

Multiply $a$ by $1$ .

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

Add $b a$ and $a b$ .

Reorder $b$ and $a$ .

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

Add $a b$ and $a b$ .

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

Move $b^{2}$ .

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