Simplify (3x-1)(4x+3)(x+1)

$(3 x - 1) (4 x + 3) (x + 1)$

Step 1

Expand $(3 x - 1) (4 x + 3)$ using the FOIL Method.

Apply the distributive property.

$(3 x (4 x + 3) - 1 (4 x + 3)) (x + 1)$

Apply the distributive property.

$(3 x (4 x) + 3 x \cdot 3 - 1 (4 x + 3)) (x + 1)$

Apply the distributive property.

$(3 x (4 x) + 3 x \cdot 3 - 1 (4 x) - 1 \cdot 3) (x + 1)$

Step 2

Simplify and combine like terms.

Simplify each term.

Rewrite using the commutative property of multiplication.

$(3 \cdot 4 x \cdot x + 3 x \cdot 3 - 1 (4 x) - 1 \cdot 3) (x + 1)$

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

Move $x$ .

$(3 \cdot 4 (x \cdot x) + 3 x \cdot 3 - 1 (4 x) - 1 \cdot 3) (x + 1)$

Multiply $x$ by $x$ .

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

Multiply $3$ by $4$ .

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

Multiply $3$ by $3$ .

$(12 x^{2} + 9 x - 1 (4 x) - 1 \cdot 3) (x + 1)$

Multiply $4$ by $- 1$ .

$(12 x^{2} + 9 x - 4 x - 1 \cdot 3) (x + 1)$

Multiply $- 1$ by $3$ .

$(12 x^{2} + 9 x - 4 x - 3) (x + 1)$

Subtract $4 x$ from $9 x$ .

$(12 x^{2} + 5 x - 3) (x + 1)$

Step 3

Expand $(12 x^{2} + 5 x - 3) (x + 1)$ by multiplying each term in the first expression by each term in the second expression.

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

Step 4

Simplify terms.

Simplify each term.

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

Move $x$ .

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

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

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

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

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

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

Add $1$ and $2$ .

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

Multiply $12$ by $1$ .

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

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

Move $x$ .

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

Multiply $x$ by $x$ .

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

Multiply $5$ by $1$ .

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

Multiply $- 3$ by $1$ .

$12 x^{3} + 12 x^{2} + 5 x^{2} + 5 x - 3 x - 3$

Simplify by adding terms.

Add $12 x^{2}$ and $5 x^{2}$ .

$12 x^{3} + 17 x^{2} + 5 x - 3 x - 3$

Subtract $3 x$ from $5 x$ .

$12 x^{3} + 17 x^{2} + 2 x - 3$

Simplify (3x-1)(4x+3)(x+1)

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