Solve (1-2u^2 u^4)*(1-u^2)

Question

Simplify the expression

1 - u^{2} - 2 u^{6} + 2 u^{8}

Evaluate

(1 - 2 u^{2} \times u^{4}) (1 - u^{2})

Multiply

More Steps

Evaluate

2 u^{2} \times u^{4}

Multiply the terms with the same base by adding their exponents

2 u^{2 + 4}

Add the numbers

2 u^{6}

(1 - 2 u^{6}) (1 - u^{2})

Apply the distributive property

1 \times 1 - 1 \times u^{2} - 2 u^{6} \times 1 - (- 2 u^{6} \times u^{2})

Any expression multiplied by 1 remains the same

1 - 1 \times u^{2} - 2 u^{6} \times 1 - (- 2 u^{6} \times u^{2})

Any expression multiplied by 1 remains the same

1 - u^{2} - 2 u^{6} \times 1 - (- 2 u^{6} \times u^{2})

Any expression multiplied by 1 remains the same

1 - u^{2} - 2 u^{6} - (- 2 u^{6} \times u^{2})

Multiply the terms

More Steps

Evaluate

u^{6} \times u^{2}

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

u^{6 + 2}

Add the numbers

u^{8}

1 - u^{2} - 2 u^{6} - (- 2 u^{8})

Solution

1 - u^{2} - 2 u^{6} + 2 u^{8}

Show Solution

Factor the expression

(1 - 2 u^{6}) (1 - u) (1 + u)

Evaluate

(1 - 2 u^{2} \times u^{4}) (1 - u^{2})

Multiply

More Steps

Evaluate

2 u^{2} \times u^{4}

Multiply the terms with the same base by adding their exponents

2 u^{2 + 4}

Add the numbers

2 u^{6}

(1 - 2 u^{6}) (1 - u^{2})

Solution

(1 - 2 u^{6}) (1 - u) (1 + u)

Show Solution

Find the roots

u_{1} = - 1, u_{2} = - \frac{6 32}{2}, u_{3} = \frac{6 32}{2}, u_{4} = 1

Alternative Form

u_{1} = - 1, u_{2} \approx - 0.890899, u_{3} \approx 0.890899, u_{4} = 1

Evaluate

(1 - 2 u^{2} \times u^{4}) (1 - u^{2})

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

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

Multiply

More Steps

Multiply the terms

2 u^{2} \times u^{4}

Multiply the terms with the same base by adding their exponents

2 u^{2 + 4}

Add the numbers

2 u^{6}

(1 - 2 u^{6}) (1 - u^{2}) = 0

Separate the equation into 2 possible cases

1 - 2 u^{6} = 0 1 - u^{2} = 0

Solve the equation

More Steps

Evaluate

1 - 2 u^{6} = 0

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

- 2 u^{6} = 0 - 1

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

- 2 u^{6} = - 1

Change the signs on both sides of the equation

2 u^{6} = 1

Divide both sides

\frac{2 u ^{6}}{2} = \frac{1}{2}

Divide the numbers

u^{6} = \frac{1}{2}

Take the root of both sides of the equation and remember to use both positive and negative roots

u = \pm 6 \frac{1}{2}

Simplify the expression

More Steps

Evaluate

6 \frac{1}{2}

To take a root of a fraction,take the root of the numerator and denominator separately

\frac{6 1}{6 2}

Simplify the radical expression

\frac{1}{6 2}

Multiply by the Conjugate

\frac{6 2 ^{5}}{6 2 \times 6 2 ^{5}}

Simplify

\frac{6 32}{6 2 \times 6 2 ^{5}}

Multiply the numbers

\frac{6 32}{2}

u = \pm \frac{6 32}{2}

Separate the equation into 2 possible cases

u = \frac{6 32}{2} u = - \frac{6 32}{2}

u = \frac{6 32}{2} u = - \frac{6 32}{2} 1 - u^{2} = 0

Solve the equation

More Steps

Evaluate

1 - u^{2} = 0

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

- u^{2} = 0 - 1

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

- u^{2} = - 1

Change the signs on both sides of the equation

u^{2} = 1

Take the root of both sides of the equation and remember to use both positive and negative roots

u = \pm 1

Simplify the expression

u = \pm 1

Separate the equation into 2 possible cases

u = 1 u = - 1

u = \frac{6 32}{2} u = - \frac{6 32}{2} u = 1 u = - 1

Solution

u_{1} = - 1, u_{2} = - \frac{6 32}{2}, u_{3} = \frac{6 32}{2}, u_{4} = 1

Alternative Form

u_{1} = - 1, u_{2} \approx - 0.890899, u_{3} \approx 0.890899, u_{4} = 1

Show Solution