Solve y^24-1 - ScanMath

Question

Simplify the expression

4 y^{2} - 1

Evaluate

y^{2} \times 4 - 1

Solution

4 y^{2} - 1

Show Solution

(2 y - 1) (2 y + 1)

Evaluate

y^{2} \times 4 - 1

Use the commutative property to reorder the terms

4 y^{2} - 1

Rewrite the expression in exponential form

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

Solution

(2 y - 1) (2 y + 1)

Show Solution

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

Alternative Form

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

Evaluate

y^{2} \times 4 - 1

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

y^{2} \times 4 - 1 = 0

Use the commutative property to reorder the terms

4 y^{2} - 1 = 0

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

4 y^{2} = 0 + 1

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

4 y^{2} = 1

Divide both sides

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

Divide the numbers

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

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

y = \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}

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

Separate the equation into 2 possible cases

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

Solution

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

Alternative Form

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

Show Solution