Solve 4a^2 - 1/4 - ScanMath

Question

Factor the expression

\frac{1}{4} (4 a - 1) (4 a + 1)

Evaluate

4 a^{2} - \frac{1}{4}

Factor out \frac{1}{4} from the expression

\frac{1}{4} (16 a^{2} - 1)

Solution

More Steps

Evaluate

16 a^{2} - 1

Rewrite the expression in exponential form

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

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

(4 a - 1) (4 a + 1)

\frac{1}{4} (4 a - 1) (4 a + 1)

Show Solution

a_{1} = - \frac{1}{4}, a_{2} = \frac{1}{4}

Alternative Form

a_{1} = - 0.25, a_{2} = 0.25

Evaluate

4 a^{2} - \frac{1}{4}

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

4 a^{2} - \frac{1}{4} = 0

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

4 a^{2} = 0 + \frac{1}{4}

Add the terms

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

Multiply by the reciprocal

4 a^{2} \times \frac{1}{4} = \frac{1}{4} \times \frac{1}{4}

Multiply

a^{2} = \frac{1}{4} \times \frac{1}{4}

Multiply

More Steps

Evaluate

\frac{1}{4} \times \frac{1}{4}

To multiply the fractions,multiply the numerators and denominators separately

\frac{1}{4 \times 4}

Multiply the numbers

\frac{1}{16}

a^{2} = \frac{1}{16}

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

a = \pm \frac{1}{16}

Simplify the expression

More Steps

Evaluate

\frac{1}{16}

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

\frac{1}{16}

Simplify the radical expression

\frac{1}{16}

Simplify the radical expression

More Steps

Evaluate

16

Write the number in exponential form with the base of 4

4^{2}

Reduce the index of the radical and exponent with 2

4

\frac{1}{4}

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

Separate the equation into 2 possible cases

a = \frac{1}{4} a = - \frac{1}{4}

Solution

a_{1} = - \frac{1}{4}, a_{2} = \frac{1}{4}

Alternative Form

a_{1} = - 0.25, a_{2} = 0.25

Show Solution