Algebra Examples

$p^{2} - 6 - q \cdot {(p^{2} - 6)}^{2}$

Step 1

Factor $- 1$ out of $p^{2} - 6 - q \cdot {(p^{2} - 6)}^{2}$ .

Tap for more steps...

Step 1.1

Reorder the expression.

Tap for more steps...

Step 1.1.1

Move $- 6$ .

$p^{2} - q \cdot {(p^{2} - 6)}^{2} - 6$

Step 1.1.2

Reorder $p^{2}$ and $- q \cdot {(p^{2} - 6)}^{2}$ .

$- q \cdot {(p^{2} - 6)}^{2} + p^{2} - 6$

Step 1.2

Factor $- 1$ out of $- q \cdot {(p^{2} - 6)}^{2}$ .

$- (q \cdot {(p^{2} - 6)}^{2}) + p^{2} - 6$

Step 1.3

Factor $- 1$ out of $p^{2}$ .

$- (q \cdot {(p^{2} - 6)}^{2}) - 1 (- p^{2}) - 6$

Step 1.4

Rewrite $- 6$ as $- 1 (6)$ .

$- (q \cdot {(p^{2} - 6)}^{2}) - 1 (- p^{2}) - 1 (6)$

Step 1.5

Factor $- 1$ out of $- (q \cdot {(p^{2} - 6)}^{2}) - 1 (- p^{2})$ .

$- (q \cdot {(p^{2} - 6)}^{2} - p^{2}) - 1 (6)$

Step 1.6

Factor $- 1$ out of $- (q \cdot {(p^{2} - 6)}^{2} - p^{2}) - 1 (6)$ .

$- (q \cdot {(p^{2} - 6)}^{2} - p^{2} + 6)$

Step 2

Rewrite ${(p^{2} - 6)}^{2}$ as $(p^{2} - 6) (p^{2} - 6)$ .

$- (q \cdot ((p^{2} - 6) (p^{2} - 6)) - p^{2} + 6)$

Step 3

Expand $(p^{2} - 6) (p^{2} - 6)$ using the FOIL Method.

Tap for more steps...

Step 3.1

Apply the distributive property.

$- (q \cdot (p^{2} (p^{2} - 6) - 6 (p^{2} - 6)) - p^{2} + 6)$

Step 3.2

Apply the distributive property.

$- (q \cdot (p^{2} p^{2} + p^{2} \cdot - 6 - 6 (p^{2} - 6)) - p^{2} + 6)$

Step 3.3

Apply the distributive property.

$- (q \cdot (p^{2} p^{2} + p^{2} \cdot - 6 - 6 p^{2} - 6 \cdot - 6) - p^{2} + 6)$

Step 4

Simplify and combine like terms.

Tap for more steps...

Step 4.1

Simplify each term.

Tap for more steps...

Step 4.1.1

Multiply $p^{2}$ by $p^{2}$ by adding the exponents.

Tap for more steps...

Step 4.1.1.1

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$- (q \cdot (p^{2 + 2} + p^{2} \cdot - 6 - 6 p^{2} - 6 \cdot - 6) - p^{2} + 6)$

Step 4.1.1.2

Add $2$ and $2$ .

$- (q \cdot (p^{4} + p^{2} \cdot - 6 - 6 p^{2} - 6 \cdot - 6) - p^{2} + 6)$

Step 4.1.2

Move $- 6$ to the left of $p^{2}$ .

$- (q \cdot (p^{4} - 6 p^{2} - 6 p^{2} - 6 \cdot - 6) - p^{2} + 6)$

Step 4.1.3

Multiply $- 6$ by $- 6$ .

$- (q \cdot (p^{4} - 6 p^{2} - 6 p^{2} + 36) - p^{2} + 6)$

Step 4.2

Subtract $6 p^{2}$ from $- 6 p^{2}$ .

$- (q \cdot (p^{4} - 12 p^{2} + 36) - p^{2} + 6)$

$- (q (p^{4} - 12 p^{2} + 36) - p^{2} + 6)$

Step 5

Apply the distributive property.

$- (q p^{4} + q (- 12 p^{2}) + q \cdot 36 - p^{2} + 6)$

Step 6

Simplify.

Tap for more steps...

Step 6.1

Rewrite using the commutative property of multiplication.

$- (q p^{4} - 12 q p^{2} + q \cdot 36 - p^{2} + 6)$

Step 6.2

Move $36$ to the left of $q$ .

$- (q p^{4} - 12 q p^{2} + 36 \cdot q - p^{2} + 6)$

$- (q p^{4} - 12 q p^{2} + 36 q - p^{2} + 6)$