Find the Product (x-2)(3x+1)(4x-3)

$(x - 2) (3 x + 1) (4 x - 3)$

Step 1

Expand $(x - 2) (3 x + 1)$ using the FOIL Method.

Apply the distributive property.

$(x (3 x + 1) - 2 (3 x + 1)) (4 x - 3)$

Apply the distributive property.

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

Apply the distributive property.

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

Step 2

Simplify and combine like terms.

Simplify each term.

Rewrite using the commutative property of multiplication.

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

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

Move $x$ .

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

Multiply $x$ by $x$ .

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

Multiply $x$ by $1$ .

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

Multiply $3$ by $- 2$ .

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

Multiply $- 2$ by $1$ .

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

Subtract $6 x$ from $x$ .

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

Step 3

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

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

Step 4

Simplify terms.

Simplify each term.

Rewrite using the commutative property of multiplication.

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

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

Move $x$ .

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

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

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

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

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

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

Add $1$ and $2$ .

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

Multiply $3$ by $4$ .

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

Multiply $- 3$ by $3$ .

$12 x^{3} - 9 x^{2} - 5 x (4 x) - 5 x \cdot - 3 - 2 (4 x) - 2 \cdot - 3$

Rewrite using the commutative property of multiplication.

$12 x^{3} - 9 x^{2} - 5 \cdot 4 x \cdot x - 5 x \cdot - 3 - 2 (4 x) - 2 \cdot - 3$

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

Move $x$ .

$12 x^{3} - 9 x^{2} - 5 \cdot 4 (x \cdot x) - 5 x \cdot - 3 - 2 (4 x) - 2 \cdot - 3$

Multiply $x$ by $x$ .

$12 x^{3} - 9 x^{2} - 5 \cdot 4 x^{2} - 5 x \cdot - 3 - 2 (4 x) - 2 \cdot - 3$

Multiply $- 5$ by $4$ .

$12 x^{3} - 9 x^{2} - 20 x^{2} - 5 x \cdot - 3 - 2 (4 x) - 2 \cdot - 3$

Multiply $- 3$ by $- 5$ .

$12 x^{3} - 9 x^{2} - 20 x^{2} + 15 x - 2 (4 x) - 2 \cdot - 3$

Multiply $4$ by $- 2$ .

$12 x^{3} - 9 x^{2} - 20 x^{2} + 15 x - 8 x - 2 \cdot - 3$

Multiply $- 2$ by $- 3$ .

$12 x^{3} - 9 x^{2} - 20 x^{2} + 15 x - 8 x + 6$

Simplify by adding terms.

Subtract $20 x^{2}$ from $- 9 x^{2}$ .

$12 x^{3} - 29 x^{2} + 15 x - 8 x + 6$

Subtract $8 x$ from $15 x$ .

$12 x^{3} - 29 x^{2} + 7 x + 6$

Find the Product (x-2)(3x+1)(4x-3)

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