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

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

Step 1

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

Apply the distributive property.

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

Apply the distributive property.

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

Apply the distributive property.

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

Step 2

Simplify and combine like terms.

Simplify each term.

Rewrite using the commutative property of multiplication.

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

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

Move $x$ .

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

Multiply $x$ by $x$ .

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

Move $- 2$ to the left of $x$ .

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

Multiply $3 x$ by $1$ .

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

Multiply $- 2$ by $1$ .

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

Add $- 2 x$ and $3 x$ .

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

Step 3

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

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

Step 4

Simplify terms.

Simplify each term.

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

Move $x$ .

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

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

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

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

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

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

Add $1$ and $2$ .

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

Multiply $- 3$ by $3$ .

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

Multiply $x$ by $x$ .

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

Move $- 3$ to the left of $x$ .

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

Multiply $- 2$ by $- 3$ .

$(3 x^{3} - 9 x^{2} + x^{2} - 3 x - 2 x + 6) (2 x - 1)$

Simplify by adding terms.

Add $- 9 x^{2}$ and $x^{2}$ .

$(3 x^{3} - 8 x^{2} - 3 x - 2 x + 6) (2 x - 1)$

Subtract $2 x$ from $- 3 x$ .

$(3 x^{3} - 8 x^{2} - 5 x + 6) (2 x - 1)$

Step 5

Expand $(3 x^{3} - 8 x^{2} - 5 x + 6) (2 x - 1)$ by multiplying each term in the first expression by each term in the second expression.

$3 x^{3} (2 x) + 3 x^{3} \cdot - 1 - 8 x^{2} (2 x) - 8 x^{2} \cdot - 1 - 5 x (2 x) - 5 x \cdot - 1 + 6 (2 x) + 6 \cdot - 1$

Step 6

Simplify terms.

Simplify each term.

Rewrite using the commutative property of multiplication.

$3 \cdot 2 x^{3} x + 3 x^{3} \cdot - 1 - 8 x^{2} (2 x) - 8 x^{2} \cdot - 1 - 5 x (2 x) - 5 x \cdot - 1 + 6 (2 x) + 6 \cdot - 1$

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

Move $x$ .

$3 \cdot 2 (x \cdot x^{3}) + 3 x^{3} \cdot - 1 - 8 x^{2} (2 x) - 8 x^{2} \cdot - 1 - 5 x (2 x) - 5 x \cdot - 1 + 6 (2 x) + 6 \cdot - 1$

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

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

$3 \cdot 2 (x^{1} x^{3}) + 3 x^{3} \cdot - 1 - 8 x^{2} (2 x) - 8 x^{2} \cdot - 1 - 5 x (2 x) - 5 x \cdot - 1 + 6 (2 x) + 6 \cdot - 1$

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

$3 \cdot 2 x^{1 + 3} + 3 x^{3} \cdot - 1 - 8 x^{2} (2 x) - 8 x^{2} \cdot - 1 - 5 x (2 x) - 5 x \cdot - 1 + 6 (2 x) + 6 \cdot - 1$

Add $1$ and $3$ .

$3 \cdot 2 x^{4} + 3 x^{3} \cdot - 1 - 8 x^{2} (2 x) - 8 x^{2} \cdot - 1 - 5 x (2 x) - 5 x \cdot - 1 + 6 (2 x) + 6 \cdot - 1$

Multiply $3$ by $2$ .

$6 x^{4} + 3 x^{3} \cdot - 1 - 8 x^{2} (2 x) - 8 x^{2} \cdot - 1 - 5 x (2 x) - 5 x \cdot - 1 + 6 (2 x) + 6 \cdot - 1$

Multiply $- 1$ by $3$ .

$6 x^{4} - 3 x^{3} - 8 x^{2} (2 x) - 8 x^{2} \cdot - 1 - 5 x (2 x) - 5 x \cdot - 1 + 6 (2 x) + 6 \cdot - 1$

Rewrite using the commutative property of multiplication.

$6 x^{4} - 3 x^{3} - 8 \cdot 2 x^{2} x - 8 x^{2} \cdot - 1 - 5 x (2 x) - 5 x \cdot - 1 + 6 (2 x) + 6 \cdot - 1$

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

Move $x$ .

$6 x^{4} - 3 x^{3} - 8 \cdot 2 (x \cdot x^{2}) - 8 x^{2} \cdot - 1 - 5 x (2 x) - 5 x \cdot - 1 + 6 (2 x) + 6 \cdot - 1$

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

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

$6 x^{4} - 3 x^{3} - 8 \cdot 2 (x^{1} x^{2}) - 8 x^{2} \cdot - 1 - 5 x (2 x) - 5 x \cdot - 1 + 6 (2 x) + 6 \cdot - 1$

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

$6 x^{4} - 3 x^{3} - 8 \cdot 2 x^{1 + 2} - 8 x^{2} \cdot - 1 - 5 x (2 x) - 5 x \cdot - 1 + 6 (2 x) + 6 \cdot - 1$

Add $1$ and $2$ .

$6 x^{4} - 3 x^{3} - 8 \cdot 2 x^{3} - 8 x^{2} \cdot - 1 - 5 x (2 x) - 5 x \cdot - 1 + 6 (2 x) + 6 \cdot - 1$

Multiply $- 8$ by $2$ .

$6 x^{4} - 3 x^{3} - 16 x^{3} - 8 x^{2} \cdot - 1 - 5 x (2 x) - 5 x \cdot - 1 + 6 (2 x) + 6 \cdot - 1$

Multiply $- 1$ by $- 8$ .

$6 x^{4} - 3 x^{3} - 16 x^{3} + 8 x^{2} - 5 x (2 x) - 5 x \cdot - 1 + 6 (2 x) + 6 \cdot - 1$

Rewrite using the commutative property of multiplication.

$6 x^{4} - 3 x^{3} - 16 x^{3} + 8 x^{2} - 5 \cdot 2 x \cdot x - 5 x \cdot - 1 + 6 (2 x) + 6 \cdot - 1$

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

Move $x$ .

$6 x^{4} - 3 x^{3} - 16 x^{3} + 8 x^{2} - 5 \cdot 2 (x \cdot x) - 5 x \cdot - 1 + 6 (2 x) + 6 \cdot - 1$

Multiply $x$ by $x$ .

$6 x^{4} - 3 x^{3} - 16 x^{3} + 8 x^{2} - 5 \cdot 2 x^{2} - 5 x \cdot - 1 + 6 (2 x) + 6 \cdot - 1$

Multiply $- 5$ by $2$ .

$6 x^{4} - 3 x^{3} - 16 x^{3} + 8 x^{2} - 10 x^{2} - 5 x \cdot - 1 + 6 (2 x) + 6 \cdot - 1$

Multiply $- 1$ by $- 5$ .

$6 x^{4} - 3 x^{3} - 16 x^{3} + 8 x^{2} - 10 x^{2} + 5 x + 6 (2 x) + 6 \cdot - 1$

Multiply $2$ by $6$ .

$6 x^{4} - 3 x^{3} - 16 x^{3} + 8 x^{2} - 10 x^{2} + 5 x + 12 x + 6 \cdot - 1$

Multiply $6$ by $- 1$ .

$6 x^{4} - 3 x^{3} - 16 x^{3} + 8 x^{2} - 10 x^{2} + 5 x + 12 x - 6$

Simplify by adding terms.

Subtract $16 x^{3}$ from $- 3 x^{3}$ .

$6 x^{4} - 19 x^{3} + 8 x^{2} - 10 x^{2} + 5 x + 12 x - 6$

Subtract $10 x^{2}$ from $8 x^{2}$ .

$6 x^{4} - 19 x^{3} - 2 x^{2} + 5 x + 12 x - 6$

Add $5 x$ and $12 x$ .

$6 x^{4} - 19 x^{3} - 2 x^{2} + 17 x - 6$

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

Related Questions

Support LCMGCF.com by disabling your adblocker.