Simplify (3x-1)(2x^3+4x^2-5)

$(3 x - 1) (2 x^{3} + 4 x^{2} - 5)$

Step 1

Expand $(3 x - 1) (2 x^{3} + 4 x^{2} - 5)$ by multiplying each term in the first expression by each term in the second expression.

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

Step 2

Simplify terms.

Simplify each term.

Rewrite using the commutative property of multiplication.

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

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

Move $x^{3}$ .

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

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

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

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

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

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

Add $3$ and $1$ .

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

Multiply $3$ by $2$ .

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

Rewrite using the commutative property of multiplication.

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

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

Move $x^{2}$ .

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

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

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

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

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

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

Add $2$ and $1$ .

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

Multiply $3$ by $4$ .

$6 x^{4} + 12 x^{3} + 3 x \cdot - 5 - 1 (2 x^{3}) - 1 (4 x^{2}) - 1 \cdot - 5$

Multiply $- 5$ by $3$ .

$6 x^{4} + 12 x^{3} - 15 x - 1 (2 x^{3}) - 1 (4 x^{2}) - 1 \cdot - 5$

Multiply $2$ by $- 1$ .

$6 x^{4} + 12 x^{3} - 15 x - 2 x^{3} - 1 (4 x^{2}) - 1 \cdot - 5$

Multiply $4$ by $- 1$ .

$6 x^{4} + 12 x^{3} - 15 x - 2 x^{3} - 4 x^{2} - 1 \cdot - 5$

Multiply $- 1$ by $- 5$ .

$6 x^{4} + 12 x^{3} - 15 x - 2 x^{3} - 4 x^{2} + 5$

Simplify by adding terms.

Subtract $2 x^{3}$ from $12 x^{3}$ .

$6 x^{4} + 10 x^{3} - 15 x - 4 x^{2} + 5$

Move $- 15 x$ .

$6 x^{4} + 10 x^{3} - 4 x^{2} - 15 x + 5$

Simplify (3x-1)(2x^3+4x^2-5)

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