Solve (2n^2-1)^(2)

Question

Simplify the expression

4 n^{4} - 4 n^{2} + 1

Evaluate

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

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

(2 n^{2})^{2} - 2 \times 2 n^{2} \times 1 + 1^{2}

Solution

4 n^{4} - 4 n^{2} + 1

Show Solution

n_{1} = - \frac{2}{2}, n_{2} = \frac{2}{2}

Alternative Form

n_{1} \approx - 0.707107, n_{2} \approx 0.707107

Evaluate

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

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

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

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

2 n^{2} - 1 = 0

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

2 n^{2} = 0 + 1

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

2 n^{2} = 1

Divide both sides

\frac{2 n ^{2}}{2} = \frac{1}{2}

Divide the numbers

n^{2} = \frac{1}{2}

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

n = \pm \frac{1}{2}

Simplify the expression

More Steps

Evaluate

\frac{1}{2}

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

\frac{1}{2}

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}

n = \pm \frac{2}{2}

Separate the equation into 2 possible cases

n = \frac{2}{2} n = - \frac{2}{2}

Solution

n_{1} = - \frac{2}{2}, n_{2} = \frac{2}{2}

Alternative Form

n_{1} \approx - 0.707107, n_{2} \approx 0.707107

Show Solution