Simplify 4t^3u(2t^2u^2-10tu^4+2)

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

Step 1

Apply the distributive property.

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

Step 2

Simplify.

Multiply $t^{3}$ by $t^{2}$ by adding the exponents.

Move $t^{2}$ .

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

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

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

Add $2$ and $3$ .

$4 t^{5} u (2 u^{2}) + 4 t^{3} u (- 10 t u^{4}) + 4 t^{3} u \cdot 2$

Multiply $t^{3}$ by $t$ by adding the exponents.

Move $t$ .

$4 t^{5} u (2 u^{2}) + 4 (t \cdot t^{3}) u (- 10 u^{4}) + 4 t^{3} u \cdot 2$

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

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

$4 t^{5} u (2 u^{2}) + 4 (t^{1} t^{3}) u (- 10 u^{4}) + 4 t^{3} u \cdot 2$

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

$4 t^{5} u (2 u^{2}) + 4 t^{1 + 3} u (- 10 u^{4}) + 4 t^{3} u \cdot 2$

Add $1$ and $3$ .

$4 t^{5} u (2 u^{2}) + 4 t^{4} u (- 10 u^{4}) + 4 t^{3} u \cdot 2$

Multiply $2$ by $4$ .

$4 t^{5} u (2 u^{2}) + 4 t^{4} u (- 10 u^{4}) + 8 t^{3} u$

Step 3

Simplify each term.

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

Move $u^{2}$ .

$4 t^{5} (u^{2} u) \cdot 2 + 4 t^{4} u (- 10 u^{4}) + 8 t^{3} u$

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

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

$4 t^{5} (u^{2} u^{1}) \cdot 2 + 4 t^{4} u (- 10 u^{4}) + 8 t^{3} u$

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

$4 t^{5} u^{2 + 1} \cdot 2 + 4 t^{4} u (- 10 u^{4}) + 8 t^{3} u$

Add $2$ and $1$ .

$4 t^{5} u^{3} \cdot 2 + 4 t^{4} u (- 10 u^{4}) + 8 t^{3} u$

Multiply $2$ by $4$ .

$8 t^{5} u^{3} + 4 t^{4} u (- 10 u^{4}) + 8 t^{3} u$

Multiply $u$ by $u^{4}$ by adding the exponents.

Move $u^{4}$ .

$8 t^{5} u^{3} + 4 t^{4} (u^{4} u) \cdot - 10 + 8 t^{3} u$

Multiply $u^{4}$ by $u$ .

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

$8 t^{5} u^{3} + 4 t^{4} (u^{4} u^{1}) \cdot - 10 + 8 t^{3} u$

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

$8 t^{5} u^{3} + 4 t^{4} u^{4 + 1} \cdot - 10 + 8 t^{3} u$

Add $4$ and $1$ .

$8 t^{5} u^{3} + 4 t^{4} u^{5} \cdot - 10 + 8 t^{3} u$

Multiply $- 10$ by $4$ .

$8 t^{5} u^{3} - 40 t^{4} u^{5} + 8 t^{3} u$

Simplify 4t^3u(2t^2u^2-10tu^4+2)

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