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

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

Step 1

Expand $(5 x^{3} - 2 x) (3 x^{2} + x - 8)$ by multiplying each term in the first expression by each term in the second expression.

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

Step 2

Simplify terms.

Simplify each term.

Rewrite using the commutative property of multiplication.

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

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

Move $x^{2}$ .

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

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

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

Add $2$ and $3$ .

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

Multiply $5$ by $3$ .

$15 x^{5} + 5 x^{3} x + 5 x^{3} \cdot - 8 - 2 x (3 x^{2}) - 2 x \cdot x - 2 x \cdot - 8$

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

Move $x$ .

$15 x^{5} + 5 (x \cdot x^{3}) + 5 x^{3} \cdot - 8 - 2 x (3 x^{2}) - 2 x \cdot x - 2 x \cdot - 8$

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

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

$15 x^{5} + 5 (x^{1} x^{3}) + 5 x^{3} \cdot - 8 - 2 x (3 x^{2}) - 2 x \cdot x - 2 x \cdot - 8$

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

$15 x^{5} + 5 x^{1 + 3} + 5 x^{3} \cdot - 8 - 2 x (3 x^{2}) - 2 x \cdot x - 2 x \cdot - 8$

Add $1$ and $3$ .

$15 x^{5} + 5 x^{4} + 5 x^{3} \cdot - 8 - 2 x (3 x^{2}) - 2 x \cdot x - 2 x \cdot - 8$

Multiply $- 8$ by $5$ .

$15 x^{5} + 5 x^{4} - 40 x^{3} - 2 x (3 x^{2}) - 2 x \cdot x - 2 x \cdot - 8$

Rewrite using the commutative property of multiplication.

$15 x^{5} + 5 x^{4} - 40 x^{3} - 2 \cdot 3 x \cdot x^{2} - 2 x \cdot x - 2 x \cdot - 8$

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

Move $x^{2}$ .

$15 x^{5} + 5 x^{4} - 40 x^{3} - 2 \cdot 3 (x^{2} x) - 2 x \cdot x - 2 x \cdot - 8$

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

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

$15 x^{5} + 5 x^{4} - 40 x^{3} - 2 \cdot 3 (x^{2} x^{1}) - 2 x \cdot x - 2 x \cdot - 8$

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

$15 x^{5} + 5 x^{4} - 40 x^{3} - 2 \cdot 3 x^{2 + 1} - 2 x \cdot x - 2 x \cdot - 8$

Add $2$ and $1$ .

$15 x^{5} + 5 x^{4} - 40 x^{3} - 2 \cdot 3 x^{3} - 2 x \cdot x - 2 x \cdot - 8$

Multiply $- 2$ by $3$ .

$15 x^{5} + 5 x^{4} - 40 x^{3} - 6 x^{3} - 2 x \cdot x - 2 x \cdot - 8$

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

Move $x$ .

$15 x^{5} + 5 x^{4} - 40 x^{3} - 6 x^{3} - 2 (x \cdot x) - 2 x \cdot - 8$

Multiply $x$ by $x$ .

$15 x^{5} + 5 x^{4} - 40 x^{3} - 6 x^{3} - 2 x^{2} - 2 x \cdot - 8$

Multiply $- 8$ by $- 2$ .

$15 x^{5} + 5 x^{4} - 40 x^{3} - 6 x^{3} - 2 x^{2} + 16 x$

Subtract $6 x^{3}$ from $- 40 x^{3}$ .

$15 x^{5} + 5 x^{4} - 46 x^{3} - 2 x^{2} + 16 x$

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

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