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

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

Expand $(3 x + 1) (x - 1)$ using the FOIL Method.

Apply the distributive property.

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

Apply the distributive property.

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

Apply the distributive property.

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

Simplify and combine like terms.

Simplify each term.

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

Move $x$ .

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

Multiply $x$ by $x$ .

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

Multiply $- 1$ by $3$ .

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

Multiply $x$ by $1$ .

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

Multiply $- 1$ by $1$ .

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

Add $- 3 x$ and $x$ .

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

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

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

Simplify terms.

Simplify each term.

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

Move $x$ .

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

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

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

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

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

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

Add $1$ and $2$ .

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

Multiply $2$ by $3$ .

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

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

Move $x$ .

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

Multiply $x$ by $x$ .

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

Multiply $2$ by $- 2$ .

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

Rewrite $- 1 x$ as $- x$ .

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

Multiply $- 1$ by $2$ .

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

Simplify by adding terms.

Subtract $2 x^{2}$ from $6 x^{2}$ .

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

Subtract $x$ from $- 4 x$ .

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

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

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

Simplify terms.

Simplify each term.

Rewrite using the commutative property of multiplication.

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

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

Move $x$ .

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

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

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

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

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

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

Add $1$ and $3$ .

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

Multiply $3$ by $2$ .

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

Multiply $5$ by $3$ .

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

Rewrite using the commutative property of multiplication.

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

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

Move $x$ .

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

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

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

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

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

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

Add $1$ and $2$ .

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

Multiply $4$ by $2$ .

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

Multiply $5$ by $4$ .

$6 x^{4} + 15 x^{3} + 8 x^{3} + 20 x^{2} - 5 x (2 x) - 5 x \cdot 5 - 2 (2 x) - 2 \cdot 5$

Rewrite using the commutative property of multiplication.

$6 x^{4} + 15 x^{3} + 8 x^{3} + 20 x^{2} - 5 \cdot 2 x \cdot x - 5 x \cdot 5 - 2 (2 x) - 2 \cdot 5$

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

Move $x$ .

$6 x^{4} + 15 x^{3} + 8 x^{3} + 20 x^{2} - 5 \cdot 2 (x \cdot x) - 5 x \cdot 5 - 2 (2 x) - 2 \cdot 5$

Multiply $x$ by $x$ .

$6 x^{4} + 15 x^{3} + 8 x^{3} + 20 x^{2} - 5 \cdot 2 x^{2} - 5 x \cdot 5 - 2 (2 x) - 2 \cdot 5$

Multiply $- 5$ by $2$ .

$6 x^{4} + 15 x^{3} + 8 x^{3} + 20 x^{2} - 10 x^{2} - 5 x \cdot 5 - 2 (2 x) - 2 \cdot 5$

Multiply $5$ by $- 5$ .

$6 x^{4} + 15 x^{3} + 8 x^{3} + 20 x^{2} - 10 x^{2} - 25 x - 2 (2 x) - 2 \cdot 5$

Multiply $2$ by $- 2$ .

$6 x^{4} + 15 x^{3} + 8 x^{3} + 20 x^{2} - 10 x^{2} - 25 x - 4 x - 2 \cdot 5$

Multiply $- 2$ by $5$ .

$6 x^{4} + 15 x^{3} + 8 x^{3} + 20 x^{2} - 10 x^{2} - 25 x - 4 x - 10$

Simplify by adding terms.

Add $15 x^{3}$ and $8 x^{3}$ .

$6 x^{4} + 23 x^{3} + 20 x^{2} - 10 x^{2} - 25 x - 4 x - 10$

Subtract $10 x^{2}$ from $20 x^{2}$ .

$6 x^{4} + 23 x^{3} + 10 x^{2} - 25 x - 4 x - 10$

Subtract $4 x$ from $- 25 x$ .

$6 x^{4} + 23 x^{3} + 10 x^{2} - 29 x - 10$

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

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