Solve (x^2 - 4x^6)^2

Question

Simplify the expression

x^{4} - 8 x^{8} + 16 x^{12}

Evaluate

(x^{2} - 4 x^{6})^{2}

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

(x^{2})^{2} - 2 x^{2} \times 4 x^{6} + (4 x^{6})^{2}

Solution

x^{4} - 8 x^{8} + 16 x^{12}

Show Solution

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

Evaluate

(x^{2} - 4 x^{6})^{2}

Factor the expression

More Steps

Evaluate

x^{2} - 4 x^{6}

Rewrite the expression

x^{2} - x^{2} \times 4 x^{4}

Factor out x^{2} from the expression

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

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

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

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

Solution

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

Show Solution

x_{1} = - \frac{2}{2}, x_{2} = 0, x_{3} = \frac{2}{2}

Alternative Form

x_{1} \approx - 0.707107, x_{2} = 0, x_{3} \approx 0.707107

Evaluate

(x^{2} - 4 x^{6})^{2}

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

(x^{2} - 4 x^{6})^{2} = 0

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

x^{2} - 4 x^{6} = 0

Factor the expression

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

Separate the equation into 2 possible cases

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

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

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

Solve the equation

More Steps

Evaluate

1 - 4 x^{4} = 0

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

- 4 x^{4} = 0 - 1

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

- 4 x^{4} = - 1

Change the signs on both sides of the equation

4 x^{4} = 1

Divide both sides

\frac{4 x ^{4}}{4} = \frac{1}{4}

Divide the numbers

x^{4} = \frac{1}{4}

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

x = \pm 4 \frac{1}{4}

Simplify the expression

More Steps

Evaluate

4 \frac{1}{4}

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

\frac{4 1}{4 4}

Simplify the radical expression

\frac{1}{4 4}

Simplify the radical expression

\frac{1}{2}

Multiply by the Conjugate

\frac{2}{2 \times 2}

When a square root of an expression is multiplied by itself,the result is that expression

\frac{2}{2}

x = \pm \frac{2}{2}

Separate the equation into 2 possible cases

x = \frac{2}{2} x = - \frac{2}{2}

x = 0 x = \frac{2}{2} x = - \frac{2}{2}

Solution

x_{1} = - \frac{2}{2}, x_{2} = 0, x_{3} = \frac{2}{2}

Alternative Form

x_{1} \approx - 0.707107, x_{2} = 0, x_{3} \approx 0.707107

Show Solution