Algebra Examples

$2 (2 - 5 t) + t^{2} (t - 1) - (t^{4} - 1)$

Step 1

Simplify each term.

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Step 1.1

Apply the distributive property.

$2 \cdot 2 + 2 (- 5 t) + t^{2} (t - 1) - (t^{4} - 1)$

Step 1.2

Multiply $2$ by $2$ .

$4 + 2 (- 5 t) + t^{2} (t - 1) - (t^{4} - 1)$

Step 1.3

Multiply $- 5$ by $2$ .

$4 - 10 t + t^{2} (t - 1) - (t^{4} - 1)$

Step 1.4

Apply the distributive property.

$4 - 10 t + t^{2} t + t^{2} \cdot - 1 - (t^{4} - 1)$

Step 1.5

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

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Step 1.5.1

Multiply $t^{2}$ by $t$ .

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Step 1.5.1.1

Raise $t$ to the power of $1$ .

$4 - 10 t + t^{2} t^{1} + t^{2} \cdot - 1 - (t^{4} - 1)$

Step 1.5.1.2

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

$4 - 10 t + t^{2 + 1} + t^{2} \cdot - 1 - (t^{4} - 1)$

Step 1.5.2

Add $2$ and $1$ .

$4 - 10 t + t^{3} + t^{2} \cdot - 1 - (t^{4} - 1)$

Step 1.6

Move $- 1$ to the left of $t^{2}$ .

$4 - 10 t + t^{3} - 1 \cdot t^{2} - (t^{4} - 1)$

Step 1.7

Rewrite $- 1 t^{2}$ as $- t^{2}$ .

$4 - 10 t + t^{3} - t^{2} - (t^{4} - 1)$

Step 1.8

Apply the distributive property.

$4 - 10 t + t^{3} - t^{2} - t^{4} - - 1$

Step 1.9

Multiply $- 1$ by $- 1$ .

$4 - 10 t + t^{3} - t^{2} - t^{4} + 1$

Step 2

Simplify the expression.

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Step 2.1

Add $4$ and $1$ .

$- 10 t + t^{3} - t^{2} - t^{4} + 5$

Step 2.2

Move $- 10 t$ .

$t^{3} - t^{2} - t^{4} - 10 t + 5$

Step 2.3

Move $- t^{2}$ .

$t^{3} - t^{4} - t^{2} - 10 t + 5$

Step 2.4

Reorder $t^{3}$ and $- t^{4}$ .

$- t^{4} + t^{3} - t^{2} - 10 t + 5$