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

Question

Simplify the expression

x^{7} - 2 x^{6} + x^{5}

Evaluate

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

Remove the parentheses

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

Rewrite the expression

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

Multiply the terms with the same base by adding their exponents

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

Add the numbers

x^{5} (x - 1)^{2}

Expand the expression

More Steps

Evaluate

(x - 1)^{2}

Use (a - b)^{2} = a^{2} - 2 ab + b^{2} to expand the expression

x^{2} - 2 x \times 1 + 1^{2}

Calculate

x^{2} - 2 x + 1

x^{5} (x^{2} - 2 x + 1)

Apply the distributive property

x^{5} \times x^{2} - x^{5} \times 2 x + x^{5} \times 1

Multiply the terms

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Evaluate

x^{5} \times x^{2}

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

x^{5 + 2}

Add the numbers

x^{7}

x^{7} - x^{5} \times 2 x + x^{5} \times 1

Multiply the terms

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Evaluate

x^{5} \times 2 x

Use the commutative property to reorder the terms

2 x^{5} \times x

Multiply the terms

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Evaluate

x^{5} \times x

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

x^{5 + 1}

Add the numbers

x^{6}

2 x^{6}

x^{7} - 2 x^{6} + x^{5} \times 1

Solution

x^{7} - 2 x^{6} + x^{5}

Show Solution

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

Evaluate

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

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

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

Calculate

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

Any expression multiplied by 1 remains the same

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

Calculate

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

Multiply

More Steps

Multiply the terms

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

Multiply the terms with the same base by adding their exponents

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

Add the numbers

x^{5} (x - 1)^{2}

x^{5} (x - 1)^{2} = 0

Separate the equation into 2 possible cases

x^{5} = 0 (x - 1)^{2} = 0

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

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

Solve the equation

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Evaluate

(x - 1)^{2} = 0

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

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

Solution

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

Show Solution