Algebra Examples

$(7 t^{2} + 6 t - 1) - (3 t - 5 t^{2} + 4 - t^{3})$

Step 1

Simplify each term.

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Step 1.1

Apply the distributive property.

$7 t^{2} + 6 t - 1 - (3 t) - (- 5 t^{2}) - 1 \cdot 4 - - t^{3}$

Step 1.2

Simplify.

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Step 1.2.1

Multiply $3$ by $- 1$ .

$7 t^{2} + 6 t - 1 - 3 t - (- 5 t^{2}) - 1 \cdot 4 - - t^{3}$

Step 1.2.2

Multiply $- 5$ by $- 1$ .

$7 t^{2} + 6 t - 1 - 3 t + 5 t^{2} - 1 \cdot 4 - - t^{3}$

Step 1.2.3

Multiply $- 1$ by $4$ .

$7 t^{2} + 6 t - 1 - 3 t + 5 t^{2} - 4 - - t^{3}$

Step 1.2.4

Multiply $- - t^{3}$ .

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Step 1.2.4.1

Multiply $- 1$ by $- 1$ .

$7 t^{2} + 6 t - 1 - 3 t + 5 t^{2} - 4 + 1 t^{3}$

Step 1.2.4.2

Multiply $t^{3}$ by $1$ .

$7 t^{2} + 6 t - 1 - 3 t + 5 t^{2} - 4 + t^{3}$

Step 2

Simplify by adding terms.

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Step 2.1

Add $7 t^{2}$ and $5 t^{2}$ .

$12 t^{2} + 6 t - 1 - 3 t - 4 + t^{3}$

Step 2.2

Subtract $3 t$ from $6 t$ .

$12 t^{2} + 3 t - 1 - 4 + t^{3}$

Step 2.3

Simplify the expression.

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Step 2.3.1

Subtract $4$ from $- 1$ .

$12 t^{2} + 3 t - 5 + t^{3}$

Step 2.3.2

Move $- 5$ .

$12 t^{2} + 3 t + t^{3} - 5$

Step 2.3.3

Move $3 t$ .

$12 t^{2} + t^{3} + 3 t - 5$

Step 2.3.4

Reorder $12 t^{2}$ and $t^{3}$ .

$t^{3} + 12 t^{2} + 3 t - 5$