Simplify -3x(5x+1)(8-2x)

$- 3 x (5 x + 1) (8 - 2 x)$

Step 1

Simplify terms.

Apply the distributive property.

$(- 3 x (5 x) - 3 x \cdot 1) (8 - 2 x)$

Simplify the expression.

Rewrite using the commutative property of multiplication.

$(- 3 \cdot 5 x \cdot x - 3 x \cdot 1) (8 - 2 x)$

Multiply $- 3$ by $1$ .

$(- 3 \cdot 5 x \cdot x - 3 x) (8 - 2 x)$

Simplify each term.

Multiply $x$ by $x$ by adding the exponents.

Move $x$ .

$(- 3 \cdot 5 (x \cdot x) - 3 x) (8 - 2 x)$

Multiply $x$ by $x$ .

$(- 3 \cdot 5 x^{2} - 3 x) (8 - 2 x)$

Multiply $- 3$ by $5$ .

$(- 15 x^{2} - 3 x) (8 - 2 x)$

Step 2

Expand $(- 15 x^{2} - 3 x) (8 - 2 x)$ using the FOIL Method.

Apply the distributive property.

$- 15 x^{2} (8 - 2 x) - 3 x (8 - 2 x)$

Apply the distributive property.

$- 15 x^{2} \cdot 8 - 15 x^{2} (- 2 x) - 3 x (8 - 2 x)$

Apply the distributive property.

$- 15 x^{2} \cdot 8 - 15 x^{2} (- 2 x) - 3 x \cdot 8 - 3 x (- 2 x)$

Step 3

Simplify and combine like terms.

Simplify each term.

Multiply $8$ by $- 15$ .

$- 120 x^{2} - 15 x^{2} (- 2 x) - 3 x \cdot 8 - 3 x (- 2 x)$

Rewrite using the commutative property of multiplication.

$- 120 x^{2} - 15 \cdot - 2 x^{2} x - 3 x \cdot 8 - 3 x (- 2 x)$

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

Move $x$ .

$- 120 x^{2} - 15 \cdot - 2 (x \cdot x^{2}) - 3 x \cdot 8 - 3 x (- 2 x)$

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

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

$- 120 x^{2} - 15 \cdot - 2 (x^{1} x^{2}) - 3 x \cdot 8 - 3 x (- 2 x)$

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

$- 120 x^{2} - 15 \cdot - 2 x^{1 + 2} - 3 x \cdot 8 - 3 x (- 2 x)$

Add $1$ and $2$ .

$- 120 x^{2} - 15 \cdot - 2 x^{3} - 3 x \cdot 8 - 3 x (- 2 x)$

Multiply $- 15$ by $- 2$ .

$- 120 x^{2} + 30 x^{3} - 3 x \cdot 8 - 3 x (- 2 x)$

Multiply $8$ by $- 3$ .

$- 120 x^{2} + 30 x^{3} - 24 x - 3 x (- 2 x)$

Rewrite using the commutative property of multiplication.

$- 120 x^{2} + 30 x^{3} - 24 x - 3 \cdot - 2 x \cdot x$

Multiply $x$ by $x$ by adding the exponents.

Move $x$ .

$- 120 x^{2} + 30 x^{3} - 24 x - 3 \cdot - 2 (x \cdot x)$

Multiply $x$ by $x$ .

$- 120 x^{2} + 30 x^{3} - 24 x - 3 \cdot - 2 x^{2}$

Multiply $- 3$ by $- 2$ .

$- 120 x^{2} + 30 x^{3} - 24 x + 6 x^{2}$

Add $- 120 x^{2}$ and $6 x^{2}$ .

$- 114 x^{2} + 30 x^{3} - 24 x$

Step 4

Reorder $- 114 x^{2}$ and $30 x^{3}$ .

$30 x^{3} - 114 x^{2} - 24 x$

Simplify -3x(5x+1)(8-2x)

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