Algebra Examples

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

Step 1

Simplify each term.

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Step 1.1

Apply the distributive property.

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

Step 1.2

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

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

Step 1.3

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

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Step 1.3.1

Apply the distributive property.

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

Step 1.3.2

Apply the distributive property.

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

Step 1.3.3

Apply the distributive property.

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

Step 1.4

Simplify and combine like terms.

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Step 1.4.1

Simplify each term.

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Step 1.4.1.1

Multiply $b$ by $b$ .

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

Step 1.4.1.2

Rewrite using the commutative property of multiplication.

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

Step 1.4.1.3

Rewrite using the commutative property of multiplication.

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

Step 1.4.1.4

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

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Step 1.4.1.4.1

Move $a$ .

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

Step 1.4.1.4.2

Multiply $a$ by $a$ .

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

Step 1.4.1.5

Multiply $- 1$ by $- 1$ .

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

Step 1.4.1.6

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

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

Step 1.4.2

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

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Step 1.4.2.1

Move $b$ .

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

Step 1.4.2.2

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

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

Step 1.5

Apply the distributive property.

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

Step 1.6

Multiply $- 2$ by $3$ .

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

Step 2

Reorder.

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Step 2.1

Move $3 b^{2}$ .

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

Step 2.2

Move $- 6 a b$ .

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