Solve (x-1)(x 1) (x-2)(x^2)

Question

Simplify the expression

x^{5} - 3 x^{4} + 2 x^{3}

Evaluate

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

Remove the parentheses

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

Rewrite the expression

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

Multiply the terms with the same base by adding their exponents

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

Add the numbers

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

Multiply the first two terms

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

Multiply the terms

More Steps

Evaluate

x^{3} (x - 1)

Apply the distributive property

x^{3} \times x - x^{3} \times 1

Multiply the terms

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Evaluate

x^{3} \times x

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

x^{3 + 1}

Add the numbers

x^{4}

x^{4} - x^{3} \times 1

Any expression multiplied by 1 remains the same

x^{4} - x^{3}

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

Apply the distributive property

x^{4} \times x - x^{4} \times 2 - x^{3} \times x - (- x^{3} \times 2)

Multiply the terms

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Evaluate

x^{4} \times x

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

x^{4 + 1}

Add the numbers

x^{5}

x^{5} - x^{4} \times 2 - x^{3} \times x - (- x^{3} \times 2)

Use the commutative property to reorder the terms

x^{5} - 2 x^{4} - x^{3} \times x - (- x^{3} \times 2)

Multiply the terms

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Evaluate

x^{3} \times x

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

x^{3 + 1}

Add the numbers

x^{4}

x^{5} - 2 x^{4} - x^{4} - (- x^{3} \times 2)

Use the commutative property to reorder the terms

x^{5} - 2 x^{4} - x^{4} - (- 2 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

x^{5} - 2 x^{4} - x^{4} + 2 x^{3}

Solution

More Steps

Evaluate

- 2 x^{4} - x^{4}

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

(- 2 - 1) x^{4}

Subtract the numbers

- 3 x^{4}

x^{5} - 3 x^{4} + 2 x^{3}

Show Solution

Find the roots

x_{1} = 0, x_{2} = 1, x_{3} = 2

Evaluate

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

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

(x - 1) (x \times 1) (x - 2) (x^{2}) = 0

Any expression multiplied by 1 remains the same

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

Calculate

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

Multiply the terms

More Steps

Multiply the terms

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

Multiply the terms with the same base by adding their exponents

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

Add the numbers

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

Multiply the first two terms

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

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

Separate the equation into 3 possible cases

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

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

x = 0 x - 1 = 0 x - 2 = 0

Solve the equation

More Steps

Evaluate

x - 1 = 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

x = 0 x = 1 x - 2 = 0

Solve the equation

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Evaluate

x - 2 = 0

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

x = 0 + 2

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

x = 2

x = 0 x = 1 x = 2

Solution

x_{1} = 0, x_{2} = 1, x_{3} = 2

Show Solution