Solve 24y^(4)-6y^(2)

Question

Factor the expression

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

Evaluate

24 y^{4} - 6 y^{2}

Factor out 6 y^{2} from the expression

6 y^{2} (4 y^{2} - 1)

Solution

More Steps

Evaluate

4 y^{2} - 1

Rewrite the expression in exponential form

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

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

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

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

Show Solution

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

Alternative Form

y_{1} = - 0.5, y_{2} = 0, y_{3} = 0.5

Evaluate

24 y^{4} - 6 y^{2}

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

24 y^{4} - 6 y^{2} = 0

Factor the expression

6 y^{2} (4 y^{2} - 1) = 0

Divide both sides

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

Separate the equation into 2 possible cases

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

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

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

Solve the equation

More Steps

Evaluate

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

\frac{1}{2}

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

Separate the equation into 2 possible cases

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

y = 0 y = \frac{1}{2} y = - \frac{1}{2}

Solution

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

Alternative Form

y_{1} = - 0.5, y_{2} = 0, y_{3} = 0.5

Show Solution