Simplify 15t(10y^3t^5+5y^2t)-2y(yt^2+4y^2)

$15 t (10 y^{3} t^{5} + 5 y^{2} t) - 2 y (y t^{2} + 4 y^{2})$

Simplify each term.

Apply the distributive property.

$15 t (10 y^{3} t^{5}) + 15 t (5 y^{2} t) - 2 y (y t^{2} + 4 y^{2})$

Multiply $t$ by $t^{5}$ by adding the exponents.

Move $t^{5}$ .

$15 (t^{5} t) (10 y^{3}) + 15 t (5 y^{2} t) - 2 y (y t^{2} + 4 y^{2})$

Multiply $t^{5}$ by $t$ .

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

$15 (t^{5} t^{1}) (10 y^{3}) + 15 t (5 y^{2} t) - 2 y (y t^{2} + 4 y^{2})$

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

$15 t^{5 + 1} (10 y^{3}) + 15 t (5 y^{2} t) - 2 y (y t^{2} + 4 y^{2})$

Add $5$ and $1$ .

$15 t^{6} (10 y^{3}) + 15 t (5 y^{2} t) - 2 y (y t^{2} + 4 y^{2})$

Multiply $t$ by $t$ by adding the exponents.

Move $t$ .

$15 t^{6} (10 y^{3}) + 15 (t \cdot t) (5 y^{2}) - 2 y (y t^{2} + 4 y^{2})$

Multiply $t$ by $t$ .

$15 t^{6} (10 y^{3}) + 15 t^{2} (5 y^{2}) - 2 y (y t^{2} + 4 y^{2})$

Simplify each term.

Rewrite using the commutative property of multiplication.

$15 \cdot 10 t^{6} y^{3} + 15 t^{2} (5 y^{2}) - 2 y (y t^{2} + 4 y^{2})$

Multiply $15$ by $10$ .

$150 t^{6} y^{3} + 15 t^{2} (5 y^{2}) - 2 y (y t^{2} + 4 y^{2})$

Rewrite using the commutative property of multiplication.

$150 t^{6} y^{3} + 15 \cdot 5 t^{2} y^{2} - 2 y (y t^{2} + 4 y^{2})$

Multiply $15$ by $5$ .

$150 t^{6} y^{3} + 75 t^{2} y^{2} - 2 y (y t^{2} + 4 y^{2})$

Apply the distributive property.

$150 t^{6} y^{3} + 75 t^{2} y^{2} - 2 y (y t^{2}) - 2 y (4 y^{2})$

Multiply $y$ by $y$ by adding the exponents.

Move $y$ .

$150 t^{6} y^{3} + 75 t^{2} y^{2} - 2 (y \cdot y) t^{2} - 2 y (4 y^{2})$

Multiply $y$ by $y$ .

$150 t^{6} y^{3} + 75 t^{2} y^{2} - 2 y^{2} t^{2} - 2 y (4 y^{2})$

Rewrite using the commutative property of multiplication.

$150 t^{6} y^{3} + 75 t^{2} y^{2} - 2 y^{2} t^{2} - 2 \cdot 4 y \cdot y^{2}$

Simplify each term.

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

Move $y^{2}$ .

$150 t^{6} y^{3} + 75 t^{2} y^{2} - 2 y^{2} t^{2} - 2 \cdot 4 (y^{2} y)$

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

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

$150 t^{6} y^{3} + 75 t^{2} y^{2} - 2 y^{2} t^{2} - 2 \cdot 4 (y^{2} y^{1})$

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

$150 t^{6} y^{3} + 75 t^{2} y^{2} - 2 y^{2} t^{2} - 2 \cdot 4 y^{2 + 1}$

Add $2$ and $1$ .

$150 t^{6} y^{3} + 75 t^{2} y^{2} - 2 y^{2} t^{2} - 2 \cdot 4 y^{3}$

Multiply $- 2$ by $4$ .

$150 t^{6} y^{3} + 75 t^{2} y^{2} - 2 y^{2} t^{2} - 8 y^{3}$

Subtract $2 y^{2} t^{2}$ from $75 t^{2} y^{2}$ .

Move $y^{2}$ .

$150 t^{6} y^{3} + 75 t^{2} y^{2} - 2 t^{2} y^{2} - 8 y^{3}$

Subtract $2 t^{2} y^{2}$ from $75 t^{2} y^{2}$ .

$150 t^{6} y^{3} + 73 t^{2} y^{2} - 8 y^{3}$

Simplify 15t(10y^3t^5+5y^2t)-2y(yt^2+4y^2)

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