Basic Math Examples

$2 \sqrt[3]{4 t^{5}} - t \sqrt[3]{32 t^{2}}$

Step 1

Simplify each term.

Tap for more steps...

Step 1.1

Rewrite $4 t^{5}$ as $t^{3} \cdot (4 t^{2})$ .

Tap for more steps...

Step 1.1.1

Factor out $t^{3}$ .

$2 \sqrt[3]{4 (t^{3} t^{2})} - t \sqrt[3]{32 t^{2}}$

Step 1.1.2

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

$2 \sqrt[3]{t^{3} \cdot 4 t^{2}} - t \sqrt[3]{32 t^{2}}$

Step 1.1.3

Add parentheses.

$2 \sqrt[3]{t^{3} \cdot (4 t^{2})} - t \sqrt[3]{32 t^{2}}$

Step 1.2

Pull terms out from under the radical.

$2 (t \sqrt[3]{4 t^{2}}) - t \sqrt[3]{32 t^{2}}$

Step 1.3

Rewrite $32 t^{2}$ as $2^{3} \cdot (4 t^{2})$ .

Tap for more steps...

Step 1.3.1

Factor $8$ out of $32$ .

$2 t \sqrt[3]{4 t^{2}} - t \sqrt[3]{8 (4) t^{2}}$

Step 1.3.2

Rewrite $8$ as $2^{3}$ .

$2 t \sqrt[3]{4 t^{2}} - t \sqrt[3]{2^{3} \cdot 4 t^{2}}$

Step 1.3.3

Add parentheses.

$2 t \sqrt[3]{4 t^{2}} - t \sqrt[3]{2^{3} \cdot (4 t^{2})}$

Step 1.4

Pull terms out from under the radical.

$2 t \sqrt[3]{4 t^{2}} - t (2 \sqrt[3]{4 t^{2}})$

Step 1.5

Multiply $2$ by $- 1$ .

$2 t \sqrt[3]{4 t^{2}} - 2 t \sqrt[3]{4 t^{2}}$

Step 2

Subtract $2 t \sqrt[3]{4 t^{2}}$ from $2 t \sqrt[3]{4 t^{2}}$ .

$0$