Precalculus Examples

$x - \sin (x) - x (x - \cos (x))$

Step 1

Simplify each term.

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Step 1.1

Apply the distributive property.

$x - \sin (x) - x \cdot x - x (- \cos (x))$

Step 1.2

Multiply $x$ by $x$ by adding the exponents.

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Step 1.2.1

Move $x$ .

$x - \sin (x) - (x \cdot x) - x (- \cos (x))$

Step 1.2.2

Multiply $x$ by $x$ .

$x - \sin (x) - x^{2} - x (- \cos (x))$

$x - \sin (x) - x^{2} - x (- \cos (x))$

Step 1.3

Multiply $- x (- \cos (x))$ .

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Step 1.3.1

Multiply $- 1$ by $- 1$ .

$x - \sin (x) - x^{2} + 1 x \cos (x)$

Step 1.3.2

Multiply $x$ by $1$ .

$x - \sin (x) - x^{2} + x \cos (x)$

$x - \sin (x) - x^{2} + x \cos (x)$

$x - \sin (x) - x^{2} + x \cos (x)$

Step 2

Simplify the expression.

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Step 2.1

Move $- \sin (x)$ .

$x - x^{2} - \sin (x) + x \cos (x)$

Step 2.2

Reorder $x$ and $- x^{2}$ .

$- x^{2} + x - \sin (x) + x \cos (x)$

$- x^{2} + x - \sin (x) + x \cos (x)$

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