Solve 3*(x-1)*(x-2)-x*(3x 1)*(1-x)

Question

Simplify the expression

- 9 x + 6 + 3 x^{3}

Evaluate

3 (x - 1) (x - 2) - x (3 x \times 1) (1 - x)

Remove the parentheses

3 (x - 1) (x - 2) - x \times 3 x \times 1 \times (1 - x)

Multiply the terms

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Multiply the terms

x \times 3 x \times 1 \times (1 - x)

Rewrite the expression

x \times 3 x (1 - x)

Multiply the terms

x^{2} \times 3 (1 - x)

Use the commutative property to reorder the terms

3 x^{2} (1 - x)

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

Expand the expression

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Calculate

3 (x - 1) (x - 2)

Simplify

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Evaluate

3 (x - 1)

Apply the distributive property

3 x - 3 \times 1

Any expression multiplied by 1 remains the same

3 x - 3

(3 x - 3) (x - 2)

Apply the distributive property

3 x \times x - 3 x \times 2 - 3 x - (- 3 \times 2)

Multiply the terms

3 x^{2} - 3 x \times 2 - 3 x - (- 3 \times 2)

Multiply the numbers

3 x^{2} - 6 x - 3 x - (- 3 \times 2)

Multiply the numbers

3 x^{2} - 6 x - 3 x - (- 6)

If a negative sign or a subtraction symbol appears outside parentheses, remove the parentheses and change the sign of every term within the parentheses

3 x^{2} - 6 x - 3 x + 6

Subtract the terms

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Evaluate

- 6 x - 3 x

Collect like terms by calculating the sum or difference of their coefficients

(- 6 - 3) x

Subtract the numbers

- 9 x

3 x^{2} - 9 x + 6

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

Expand the expression

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Calculate

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

Apply the distributive property

- 3 x^{2} \times 1 - (- 3 x^{2} \times x)

Any expression multiplied by 1 remains the same

- 3 x^{2} - (- 3 x^{2} \times x)

Multiply the terms

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Evaluate

x^{2} \times x

Use the product rule a^{n} \times a^{m} = a^{n + m} to simplify the expression

x^{2 + 1}

Add the numbers

x^{3}

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

If a negative sign or a subtraction symbol appears outside parentheses, remove the parentheses and change the sign of every term within the parentheses

- 3 x^{2} + 3 x^{3}

3 x^{2} - 9 x + 6 - 3 x^{2} + 3 x^{3}

The sum of two opposites equals 0

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Evaluate

3 x^{2} - 3 x^{2}

Collect like terms

(3 - 3) x^{2}

Add the coefficients

0 \times x^{2}

Calculate

0

0 - 9 x + 6 + 3 x^{3}

Solution

- 9 x + 6 + 3 x^{3}

Show Solution

Factor the expression

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

Evaluate

3 (x - 1) (x - 2) - x (3 x \times 1) (1 - x)

Remove the parentheses

3 (x - 1) (x - 2) - x \times 3 x \times 1 \times (1 - x)

Multiply the terms

3 (x - 1) (x - 2) - x \times 3 x (1 - x)

Multiply

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Multiply the terms

x \times 3 x (1 - x)

Multiply the terms

x^{2} \times 3 (1 - x)

Use the commutative property to reorder the terms

3 x^{2} (1 - x)

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

Rewrite the expression

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

Factor out 3 (x - 1) from the expression

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

Solution

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Evaluate

x - 2 + x^{2}

Reorder the terms

- 2 + x + x^{2}

Rewrite the expression

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

Calculate

- 2 - x + 2 x + x^{2}

Rewrite the expression

- 2 - x + x \times 2 + x \times x

Factor out - 1 from the expression

- (2 + x) + x \times 2 + x \times x

Factor out x from the expression

- (2 + x) + x (2 + x)

Factor out 2 + x from the expression

(- 1 + x) (2 + x)

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

Show Solution

Find the roots

x_{1} = - 2, x_{2} = 1

Evaluate

3 (x - 1) (x - 2) - x (3 x \times 1) (1 - x)

To find the roots of the expression,set the expression equal to 0

3 (x - 1) (x - 2) - x (3 x \times 1) (1 - x) = 0

Multiply the terms

3 (x - 1) (x - 2) - x \times 3 x (1 - x) = 0

Multiply

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Multiply the terms

x \times 3 x (1 - x)

Multiply the terms

x^{2} \times 3 (1 - x)

Use the commutative property to reorder the terms

3 x^{2} (1 - x)

3 (x - 1) (x - 2) - 3 x^{2} (1 - x) = 0

Calculate

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Evaluate

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

Expand the expression

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Calculate

3 (x - 1) (x - 2)

Simplify

(3 x - 3) (x - 2)

Apply the distributive property

3 x \times x - 3 x \times 2 - 3 x - (- 3 \times 2)

Multiply the terms

3 x^{2} - 3 x \times 2 - 3 x - (- 3 \times 2)

Multiply the numbers

3 x^{2} - 6 x - 3 x - (- 3 \times 2)

Multiply the numbers

3 x^{2} - 6 x - 3 x - (- 6)

If a negative sign or a subtraction symbol appears outside parentheses, remove the parentheses and change the sign of every term within the parentheses

3 x^{2} - 6 x - 3 x + 6

Subtract the terms

3 x^{2} - 9 x + 6

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

Expand the expression

More Steps

Calculate

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

Apply the distributive property

- 3 x^{2} \times 1 - (- 3 x^{2} \times x)

Any expression multiplied by 1 remains the same

- 3 x^{2} - (- 3 x^{2} \times x)

Multiply the terms

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

If a negative sign or a subtraction symbol appears outside parentheses, remove the parentheses and change the sign of every term within the parentheses

- 3 x^{2} + 3 x^{3}

3 x^{2} - 9 x + 6 - 3 x^{2} + 3 x^{3}

The sum of two opposites equals 0

More Steps

Evaluate

3 x^{2} - 3 x^{2}

Collect like terms

(3 - 3) x^{2}

Add the coefficients

0 \times x^{2}

Calculate

0

0 - 9 x + 6 + 3 x^{3}

Remove 0

- 9 x + 6 + 3 x^{3}

- 9 x + 6 + 3 x^{3} = 0

Factor the expression

3 (1 - x)^{2} (2 + x) = 0

Divide both sides

(1 - x)^{2} (2 + x) = 0

Separate the equation into 2 possible cases

(1 - x)^{2} = 0 2 + x = 0

Solve the equation

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Evaluate

(1 - x)^{2} = 0

The only way a power can be 0 is when the base equals 0

1 - x = 0

Move the constant to the right-hand side and change its sign

- x = 0 - 1

Removing 0 doesn't change the value,so remove it from the expression

- x = - 1

Change the signs on both sides of the equation

x = 1

x = 1 2 + x = 0

Solve the equation

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Evaluate

2 + x = 0

Move the constant to the right side

x = 0 - 2

Removing 0 doesn't change the value,so remove it from the expression

x = - 2

x = 1 x = - 2

Solution

x_{1} = - 2, x_{2} = 1

Show Solution