Basic Math Examples

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

Step 1

Rewrite ${(a - 3 b)}^{2}$ as $(a - 3 b) (a - 3 b)$ .

$1 + (a - 3 b) (a - 3 b)$

Step 2

Expand $(a - 3 b) (a - 3 b)$ using the FOIL Method.

Tap for more steps...

Step 2.1

Apply the distributive property.

$1 + a (a - 3 b) - 3 b (a - 3 b)$

Step 2.2

Apply the distributive property.

$1 + a \cdot a + a (- 3 b) - 3 b (a - 3 b)$

Step 2.3

Apply the distributive property.

$1 + a \cdot a + a (- 3 b) - 3 b a - 3 b (- 3 b)$

Step 3

Simplify and combine like terms.

Tap for more steps...

Step 3.1

Simplify each term.

Tap for more steps...

Step 3.1.1

Multiply $a$ by $a$ .

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

Step 3.1.2

Rewrite using the commutative property of multiplication.

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

Step 3.1.3

Rewrite using the commutative property of multiplication.

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

Step 3.1.4

Multiply $b$ by $b$ by adding the exponents.

Tap for more steps...

Step 3.1.4.1

Move $b$ .

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

Step 3.1.4.2

Multiply $b$ by $b$ .

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

Step 3.1.5

Multiply $- 3$ by $- 3$ .

$1 + a^{2} - 3 a b - 3 b a + 9 b^{2}$

Step 3.2

Subtract $3 b a$ from $- 3 a b$ .

Tap for more steps...

Step 3.2.1

Move $b$ .

$1 + a^{2} - 3 a b - 3 a b + 9 b^{2}$

Step 3.2.2

Subtract $3 a b$ from $- 3 a b$ .

$1 + a^{2} - 6 a b + 9 b^{2}$