Simplify 5c^2(c+10)-4c(2c^2-6c+1)

$5 c^{2} (c + 10) - 4 c (2 c^{2} - 6 c + 1)$

Simplify each term.

Apply the distributive property.

$5 c^{2} c + 5 c^{2} \cdot 10 - 4 c (2 c^{2} - 6 c + 1)$

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

Move $c$ .

$5 (c \cdot c^{2}) + 5 c^{2} \cdot 10 - 4 c (2 c^{2} - 6 c + 1)$

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

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

$5 (c^{1} c^{2}) + 5 c^{2} \cdot 10 - 4 c (2 c^{2} - 6 c + 1)$

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

$5 c^{1 + 2} + 5 c^{2} \cdot 10 - 4 c (2 c^{2} - 6 c + 1)$

Add $1$ and $2$ .

$5 c^{3} + 5 c^{2} \cdot 10 - 4 c (2 c^{2} - 6 c + 1)$

Multiply $10$ by $5$ .

$5 c^{3} + 50 c^{2} - 4 c (2 c^{2} - 6 c + 1)$

Apply the distributive property.

$5 c^{3} + 50 c^{2} - 4 c (2 c^{2}) - 4 c (- 6 c) - 4 c \cdot 1$

Simplify.

Rewrite using the commutative property of multiplication.

$5 c^{3} + 50 c^{2} - 4 \cdot 2 c \cdot c^{2} - 4 c (- 6 c) - 4 c \cdot 1$

Rewrite using the commutative property of multiplication.

$5 c^{3} + 50 c^{2} - 4 \cdot 2 c \cdot c^{2} - 4 \cdot - 6 c \cdot c - 4 c \cdot 1$

Multiply $- 4$ by $1$ .

$5 c^{3} + 50 c^{2} - 4 \cdot 2 c \cdot c^{2} - 4 \cdot - 6 c \cdot c - 4 c$

Simplify each term.

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

Move $c^{2}$ .

$5 c^{3} + 50 c^{2} - 4 \cdot 2 (c^{2} c) - 4 \cdot - 6 c \cdot c - 4 c$

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

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

$5 c^{3} + 50 c^{2} - 4 \cdot 2 (c^{2} c^{1}) - 4 \cdot - 6 c \cdot c - 4 c$

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

$5 c^{3} + 50 c^{2} - 4 \cdot 2 c^{2 + 1} - 4 \cdot - 6 c \cdot c - 4 c$

Add $2$ and $1$ .

$5 c^{3} + 50 c^{2} - 4 \cdot 2 c^{3} - 4 \cdot - 6 c \cdot c - 4 c$

Multiply $- 4$ by $2$ .

$5 c^{3} + 50 c^{2} - 8 c^{3} - 4 \cdot - 6 c \cdot c - 4 c$

Multiply $c$ by $c$ by adding the exponents.

Move $c$ .

$5 c^{3} + 50 c^{2} - 8 c^{3} - 4 \cdot - 6 (c \cdot c) - 4 c$

Multiply $c$ by $c$ .

$5 c^{3} + 50 c^{2} - 8 c^{3} - 4 \cdot - 6 c^{2} - 4 c$

Multiply $- 4$ by $- 6$ .

$5 c^{3} + 50 c^{2} - 8 c^{3} + 24 c^{2} - 4 c$

Simplify by adding terms.

Subtract $8 c^{3}$ from $5 c^{3}$ .

$- 3 c^{3} + 50 c^{2} + 24 c^{2} - 4 c$

Add $50 c^{2}$ and $24 c^{2}$ .

$- 3 c^{3} + 74 c^{2} - 4 c$

Simplify 5c^2(c+10)-4c(2c^2-6c+1)

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