Algebra Examples

$(11 p - 4 q^{2} - q) - (q^{2} - 4 p + 7 p^{2})$

Step 1

Simplify each term.

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Step 1.1

Apply the distributive property.

$11 p - 4 q^{2} - q - q^{2} - (- 4 p) - (7 p^{2})$

Step 1.2

Simplify.

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Step 1.2.1

Multiply $- 4$ by $- 1$ .

$11 p - 4 q^{2} - q - q^{2} + 4 p - (7 p^{2})$

Step 1.2.2

Multiply $7$ by $- 1$ .

$11 p - 4 q^{2} - q - q^{2} + 4 p - 7 p^{2}$

$11 p - 4 q^{2} - q - q^{2} + 4 p - 7 p^{2}$

$11 p - 4 q^{2} - q - q^{2} + 4 p - 7 p^{2}$

Step 2

Simplify by adding terms.

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Step 2.1

Add $11 p$ and $4 p$ .

$- 4 q^{2} - q - q^{2} + 15 p - 7 p^{2}$

Step 2.2

Subtract $q^{2}$ from $- 4 q^{2}$ .

$- 5 q^{2} - q + 15 p - 7 p^{2}$

Step 2.3

Simplify the expression.

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Step 2.3.1

Move $- q$ .

$- 5 q^{2} + 15 p - 7 p^{2} - q$

Step 2.3.2

Move $15 p$ .

$- 5 q^{2} - 7 p^{2} + 15 p - q$

Step 2.3.3

Reorder $- 5 q^{2}$ and $- 7 p^{2}$ .

$- 7 p^{2} - 5 q^{2} + 15 p - q$

$- 7 p^{2} - 5 q^{2} + 15 p - q$

$- 7 p^{2} - 5 q^{2} + 15 p - q$

$[\begin{array}{c} x^{2} & \frac{1}{2} \\ \sqrt{π} & \int x d x \end{array}]$