Basic Math Examples

${(a + 3 b)}^{2} + b (a - 9 b) - 7 a b$

Step 1

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

$(a + 3 b) (a + 3 b) + b (a - 9 b) - 7 a b$

Step 2

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

Tap for more steps...

Step 2.1

Apply the distributive property.

$a (a + 3 b) + 3 b (a + 3 b) + b (a - 9 b) - 7 a b$

Step 2.2

Apply the distributive property.

$a \cdot a + a (3 b) + 3 b (a + 3 b) + b (a - 9 b) - 7 a b$

Step 2.3

Apply the distributive property.

$a \cdot a + a (3 b) + 3 b a + 3 b (3 b) + b (a - 9 b) - 7 a b$

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 $a$ .

$a^{2} + a (3 b) + 3 b a + 3 b (3 b) + b (a - 9 b) - 7 a b$

Step 3.1.2

Rewrite using the commutative property of multiplication.

$a^{2} + 3 a b + 3 b a + 3 b (3 b) + b (a - 9 b) - 7 a b$

Step 3.1.3

Rewrite using the commutative property of multiplication.

$a^{2} + 3 a b + 3 b a + 3 \cdot 3 b \cdot b + b (a - 9 b) - 7 a b$

Step 3.1.4

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

Tap for more steps...

Step 3.1.4.1

Move $b$ .

$a^{2} + 3 a b + 3 b a + 3 \cdot 3 (b \cdot b) + b (a - 9 b) - 7 a b$

Step 3.1.4.2

Multiply $b$ by $b$ .

$a^{2} + 3 a b + 3 b a + 3 \cdot 3 b^{2} + b (a - 9 b) - 7 a b$

Step 3.1.5

Multiply $3$ by $3$ .

$a^{2} + 3 a b + 3 b a + 9 b^{2} + b (a - 9 b) - 7 a b$

Step 3.2

Add $3 a b$ and $3 b a$ .

Tap for more steps...

Step 3.2.1

Move $b$ .

$a^{2} + 3 a b + 3 a b + 9 b^{2} + b (a - 9 b) - 7 a b$

Step 3.2.2

Add $3 a b$ and $3 a b$ .

$a^{2} + 6 a b + 9 b^{2} + b (a - 9 b) - 7 a b$

Step 4

Apply the distributive property.

$a^{2} + 6 a b + 9 b^{2} + b a + b (- 9 b) - 7 a b$

Step 5

Rewrite using the commutative property of multiplication.

$a^{2} + 6 a b + 9 b^{2} + b a - 9 b \cdot b - 7 a b$

Step 6

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

Tap for more steps...

Step 6.1

Move $b$ .

$a^{2} + 6 a b + 9 b^{2} + b a - 9 (b \cdot b) - 7 a b$

Step 6.2

Multiply $b$ by $b$ .

$a^{2} + 6 a b + 9 b^{2} + b a - 9 b^{2} - 7 a b$

Step 7

Add $6 a b$ and $b a$ .

Tap for more steps...

Step 7.1

Reorder $b$ and $a$ .

$a^{2} + 9 b^{2} + 6 a b + a b - 9 b^{2} - 7 a b$

Step 7.2

Add $6 a b$ and $a b$ .

$a^{2} + 9 b^{2} + 7 a b - 9 b^{2} - 7 a b$

Step 8

Subtract $9 b^{2}$ from $9 b^{2}$ .

$a^{2} + 7 a b + 0 - 7 a b$

Step 9

Add $a^{2}$ and $0$ .

$a^{2} + 7 a b - 7 a b$

Step 10

Subtract $7 a b$ from $7 a b$ .

$a^{2} + 0$

Step 11

Add $a^{2}$ and $0$ .

$a^{2}$