Algebra Examples

$(11 p - 6 q^{2} - q) - (q^{2} - 5 p + 7 p^{2})$

Step 1

Regroup terms.

$- q + 11 p - 6 q^{2} - (q^{2} - 5 p + 7 p^{2})$

Step 2

Factor $- 1$ out of $11 p - 6 q^{2} - (q^{2} - 5 p + 7 p^{2})$ .

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Step 2.1

Reorder the expression.

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Step 2.1.1

Move $- 5 p$ .

$- q + 11 p - 6 q^{2} - (q^{2} + 7 p^{2} - 5 p)$

Step 2.1.2

Reorder $q^{2}$ and $7 p^{2}$ .

$- q + 11 p - 6 q^{2} - (7 p^{2} + q^{2} - 5 p)$

Step 2.1.3

Move $11 p$ .

$- q - 6 q^{2} - (7 p^{2} + q^{2} - 5 p) + 11 p$

Step 2.1.4

Reorder $- 6 q^{2}$ and $- (7 p^{2} + q^{2} - 5 p)$ .

$- q - (7 p^{2} + q^{2} - 5 p) - 6 q^{2} + 11 p$

Step 2.2

Factor $- 1$ out of $- 6 q^{2}$ .

$- q - (7 p^{2} + q^{2} - 5 p) - (6 q^{2}) + 11 p$

Step 2.3

Factor $- 1$ out of $11 p$ .

$- q - (7 p^{2} + q^{2} - 5 p) - (6 q^{2}) - (- 11 p)$

Step 2.4

Factor $- 1$ out of $- (7 p^{2} + q^{2} - 5 p) - (6 q^{2})$ .

$- q - (7 p^{2} + q^{2} - 5 p + 6 q^{2}) - (- 11 p)$

Step 2.5

Factor $- 1$ out of $- (7 p^{2} + q^{2} - 5 p + 6 q^{2}) - (- 11 p)$ .

$- q - (7 p^{2} + q^{2} - 5 p + 6 q^{2} - 11 p)$

Step 3

Add $q^{2}$ and $6 q^{2}$ .

$- q - (7 p^{2} + 7 q^{2} - 5 p - 11 p)$

Step 4

Subtract $11 p$ from $- 5 p$ .

$- q - (7 p^{2} + 7 q^{2} - 16 p)$

Step 5

Factor $- 1$ out of $- q - (7 p^{2} + 7 q^{2} - 16 p)$ .

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Step 5.1

Reorder $- q$ and $- (7 p^{2} + 7 q^{2} - 16 p)$ .

$- (7 p^{2} + 7 q^{2} - 16 p) - q$

Step 5.2

Factor $- 1$ out of $- q$ .

$- (7 p^{2} + 7 q^{2} - 16 p) - (q)$

Step 5.3

Factor $- 1$ out of $- (7 p^{2} + 7 q^{2} - 16 p) - (q)$ .

$- (7 p^{2} + 7 q^{2} - 16 p + q)$