Solve x^4(1-x)^4/1 x^2

Question

Simplify the expression

x^{6} - 4 x^{7} + 6 x^{8} - 4 x^{9} + x^{10}

Evaluate

x^{4} \times \frac{( 1 - x ) ^{4}}{1} x^{2}

Divide the terms

x^{4} (1 - x)^{4} x^{2}

Multiply the terms with the same base by adding their exponents

x^{4 + 2} (1 - x)^{4}

Add the numbers

x^{6} (1 - x)^{4}

Expand the expression

x^{6} (1 - 4 x + 6 x^{2} - 4 x^{3} + x^{4})

Apply the distributive property

x^{6} \times 1 - x^{6} \times 4 x + x^{6} \times 6 x^{2} - x^{6} \times 4 x^{3} + x^{6} \times x^{4}

Any expression multiplied by 1 remains the same

x^{6} - x^{6} \times 4 x + x^{6} \times 6 x^{2} - x^{6} \times 4 x^{3} + x^{6} \times x^{4}

Multiply the terms

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Evaluate

x^{6} \times 4 x

Use the commutative property to reorder the terms

4 x^{6} \times x

Multiply the terms

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Evaluate

x^{6} \times x

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

x^{6 + 1}

Add the numbers

x^{7}

4 x^{7}

x^{6} - 4 x^{7} + x^{6} \times 6 x^{2} - x^{6} \times 4 x^{3} + x^{6} \times x^{4}

Multiply the terms

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Evaluate

x^{6} \times 6 x^{2}

Use the commutative property to reorder the terms

6 x^{6} \times x^{2}

Multiply the terms

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Evaluate

x^{6} \times x^{2}

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

x^{6 + 2}

Add the numbers

x^{8}

6 x^{8}

x^{6} - 4 x^{7} + 6 x^{8} - x^{6} \times 4 x^{3} + x^{6} \times x^{4}

Multiply the terms

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Evaluate

x^{6} \times 4 x^{3}

Use the commutative property to reorder the terms

4 x^{6} \times x^{3}

Multiply the terms

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Evaluate

x^{6} \times x^{3}

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

x^{6 + 3}

Add the numbers

x^{9}

4 x^{9}

x^{6} - 4 x^{7} + 6 x^{8} - 4 x^{9} + x^{6} \times x^{4}

Solution

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Evaluate

x^{6} \times x^{4}

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

x^{6 + 4}

Add the numbers

x^{10}

x^{6} - 4 x^{7} + 6 x^{8} - 4 x^{9} + x^{10}

Show Solution

Find the roots

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

Evaluate

x^{4} \times \frac{( 1 - x ) ^{4}}{1} x^{2}

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

x^{4} \times \frac{( 1 - x ) ^{4}}{1} x^{2} = 0

Divide the terms

x^{4} (1 - x)^{4} x^{2} = 0

Multiply

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Multiply the terms

x^{4} (1 - x)^{4} x^{2}

Multiply the terms with the same base by adding their exponents

x^{4 + 2} (1 - x)^{4}

Add the numbers

x^{6} (1 - x)^{4}

x^{6} (1 - x)^{4} = 0

Separate the equation into 2 possible cases

x^{6} = 0 (1 - x)^{4} = 0

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

x = 0 (1 - x)^{4} = 0

Solve the equation

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Evaluate

(1 - x)^{4} = 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 = 0 x = 1

Solution

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

Show Solution