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

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

Step 1

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

Apply the distributive property.

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

Apply the distributive property.

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

Apply the distributive property.

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

Step 2

Simplify and combine like terms.

Simplify each term.

Multiply $x$ by $x$ .

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

Move $- 1$ to the left of $x$ .

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

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

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

Multiply $- 2$ by $- 1$ .

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

Subtract $2 x$ from $- x$ .

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

Step 3

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

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

Step 4

Simplify terms.

Simplify each term.

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

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

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

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

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

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

Add $2$ and $1$ .

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

Move $- 1$ to the left of $x^{2}$ .

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

Rewrite $- 1 x^{2}$ as $- x^{2}$ .

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

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

Move $x$ .

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

Multiply $x$ by $x$ .

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

Multiply $- 1$ by $- 3$ .

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

Multiply $2$ by $- 1$ .

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

Simplify by adding terms.

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

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

Add $3 x$ and $2 x$ .

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

Step 5

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

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

Step 6

Simplify terms.

Simplify each term.

Rewrite using the commutative property of multiplication.

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

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

Move $x$ .

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

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

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

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

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

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

Add $1$ and $3$ .

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

Move $- 2$ to the left of $x^{3}$ .

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

Rewrite using the commutative property of multiplication.

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

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

Move $x$ .

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

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

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

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

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

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

Add $1$ and $2$ .

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

Multiply $- 4$ by $3$ .

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

Multiply $- 2$ by $- 4$ .

$3 x^{4} - 2 x^{3} - 12 x^{3} + 8 x^{2} + 5 x (3 x) + 5 x \cdot - 2 - 2 (3 x) - 2 \cdot - 2$

Rewrite using the commutative property of multiplication.

$3 x^{4} - 2 x^{3} - 12 x^{3} + 8 x^{2} + 5 \cdot 3 x \cdot x + 5 x \cdot - 2 - 2 (3 x) - 2 \cdot - 2$

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

Move $x$ .

$3 x^{4} - 2 x^{3} - 12 x^{3} + 8 x^{2} + 5 \cdot 3 (x \cdot x) + 5 x \cdot - 2 - 2 (3 x) - 2 \cdot - 2$

Multiply $x$ by $x$ .

$3 x^{4} - 2 x^{3} - 12 x^{3} + 8 x^{2} + 5 \cdot 3 x^{2} + 5 x \cdot - 2 - 2 (3 x) - 2 \cdot - 2$

Multiply $5$ by $3$ .

$3 x^{4} - 2 x^{3} - 12 x^{3} + 8 x^{2} + 15 x^{2} + 5 x \cdot - 2 - 2 (3 x) - 2 \cdot - 2$

Multiply $- 2$ by $5$ .

$3 x^{4} - 2 x^{3} - 12 x^{3} + 8 x^{2} + 15 x^{2} - 10 x - 2 (3 x) - 2 \cdot - 2$

Multiply $3$ by $- 2$ .

$3 x^{4} - 2 x^{3} - 12 x^{3} + 8 x^{2} + 15 x^{2} - 10 x - 6 x - 2 \cdot - 2$

Multiply $- 2$ by $- 2$ .

$3 x^{4} - 2 x^{3} - 12 x^{3} + 8 x^{2} + 15 x^{2} - 10 x - 6 x + 4$

Simplify by adding terms.

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

$3 x^{4} - 14 x^{3} + 8 x^{2} + 15 x^{2} - 10 x - 6 x + 4$

Add $8 x^{2}$ and $15 x^{2}$ .

$3 x^{4} - 14 x^{3} + 23 x^{2} - 10 x - 6 x + 4$

Subtract $6 x$ from $- 10 x$ .

$3 x^{4} - 14 x^{3} + 23 x^{2} - 16 x + 4$

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

Related Questions

Support LCMGCF.com by disabling your adblocker.