Precalculus Examples

$t (x) = - x$ , $p (x) = 10 x + 2$ , $p (t (3)) - t (p (3))$

Step 1

Replace the variable $x$ with $t (3)$ in the expression.

$p (t (3)) = 10 (t (3)) + 2$

Step 2

Replace the variable $x$ with $p (3)$ in the expression.

$t (p (3)) = - (p (3))$

Step 3

Replace the function designators in $p (t (3)) - t (p (3))$ with the actual functions.

$(10 (t (3)) + 2) - (- (p (3)))$

Step 4

Simplify $(10 (t (3)) + 2) - (- (p (3)))$ .

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Step 4.1

Simplify each term.

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Step 4.1.1

Move $3$ to the left of $t$ .

$10 (3 t) + 2 - (- (p (3)))$

Step 4.1.2

Multiply $3$ by $10$ .

$30 t + 2 - (- (p (3)))$

Step 4.1.3

Move $3$ to the left of $p$ .

$30 t + 2 - - (3 p)$

Step 4.1.4

Multiply $3$ by $- 1$ .

$30 t + 2 - (- 3 p)$

Step 4.1.5

Multiply $- 3$ by $- 1$ .

$30 t + 2 + 3 p$

Step 4.2

Simplify the expression.

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Step 4.2.1

Move $2$ .

$30 t + 3 p + 2$

Step 4.2.2

Reorder $30 t$ and $3 p$ .

$3 p + 30 t + 2$