Factor (a-b)*z+3(b-a)^2

$(a - b) \cdot z + 3 {(b - a)}^{2}$

Step 1

Apply the distributive property.

$a z - b z + 3 {(b - a)}^{2}$

Step 2

Rewrite ${(b - a)}^{2}$ as $(b - a) (b - a)$ .

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

Step 3

Expand $(b - a) (b - a)$ using the FOIL Method.

Apply the distributive property.

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

Apply the distributive property.

$a z - b z + 3 (b \cdot b + b (- a) - a (b - a))$

Apply the distributive property.

$a z - b z + 3 (b \cdot b + b (- a) - a b - a (- a))$

Step 4

Simplify and combine like terms.

Simplify each term.

Multiply $b$ by $b$ .

$a z - b z + 3 (b^{2} + b (- a) - a b - a (- a))$

Rewrite using the commutative property of multiplication.

$a z - b z + 3 (b^{2} - b a - a b - a (- a))$

Rewrite using the commutative property of multiplication.

$a z - b z + 3 (b^{2} - b a - a b - 1 \cdot - 1 a \cdot a)$

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

Move $a$ .

$a z - b z + 3 (b^{2} - b a - a b - 1 \cdot - 1 (a \cdot a))$

Multiply $a$ by $a$ .

$a z - b z + 3 (b^{2} - b a - a b - 1 \cdot - 1 a^{2})$

Multiply $- 1$ by $- 1$ .

$a z - b z + 3 (b^{2} - b a - a b + 1 a^{2})$

Multiply $a^{2}$ by $1$ .

$a z - b z + 3 (b^{2} - b a - a b + a^{2})$

Subtract $a b$ from $- b a$ .

Move $b$ .

$a z - b z + 3 (b^{2} - a b - a b + a^{2})$

Subtract $a b$ from $- a b$ .

$a z - b z + 3 (b^{2} - 2 a b + a^{2})$

Step 5

Apply the distributive property.

$a z - b z + 3 b^{2} + 3 (- 2 a b) + 3 a^{2}$

Step 6

Multiply $- 2$ by $3$ .

$a z - b z + 3 b^{2} - 6 (a b) + 3 a^{2}$

Step 7

Remove parentheses.

$a z - b z + 3 b^{2} - 6 a b + 3 a^{2}$

Factor (a-b)*z+3(b-a)^2

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