Solve 16n^2-4 - ScanMath

Question

Factor the expression

4 (2 n - 1) (2 n + 1)

Evaluate

16 n^{2} - 4

Factor out 4 from the expression

4 (4 n^{2} - 1)

Solution

More Steps

Evaluate

4 n^{2} - 1

Rewrite the expression in exponential form

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

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

(2 n - 1) (2 n + 1)

4 (2 n - 1) (2 n + 1)

Show Solution

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

Alternative Form

n_{1} = - 0.5, n_{2} = 0.5

Evaluate

16 n^{2} - 4

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

16 n^{2} - 4 = 0

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

16 n^{2} = 0 + 4

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

16 n^{2} = 4

Divide both sides

\frac{16 n ^{2}}{16} = \frac{4}{16}

Divide the numbers

n^{2} = \frac{4}{16}

Cancel out the common factor 4

n^{2} = \frac{1}{4}

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

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

Simplify the expression

More Steps

Evaluate

\frac{1}{4}

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

\frac{1}{4}

Simplify the radical expression

\frac{1}{4}

Simplify the radical expression

More Steps

Evaluate

4

Write the number in exponential form with the base of 2

2^{2}

Reduce the index of the radical and exponent with 2

2

\frac{1}{2}

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

Separate the equation into 2 possible cases

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

Solution

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

Alternative Form

n_{1} = - 0.5, n_{2} = 0.5

Show Solution