Solve 4y^(2)(9y^(2)-1)

Question

Simplify the expression

36 y^{4} - 4 y^{2}

Evaluate

4 y^{2} (9 y^{2} - 1)

Apply the distributive property

4 y^{2} \times 9 y^{2} - 4 y^{2} \times 1

Multiply the terms

More Steps

Evaluate

4 y^{2} \times 9 y^{2}

Multiply the numbers

36 y^{2} \times y^{2}

Multiply the terms

More Steps

Evaluate

y^{2} \times y^{2}

Use the product rule a^{n} \times a^{m} = a^{n + m} to simplify the expression

y^{2 + 2}

Add the numbers

y^{4}

36 y^{4}

36 y^{4} - 4 y^{2} \times 1

Solution

36 y^{4} - 4 y^{2}

Show Solution

4 y^{2} (3 y - 1) (3 y + 1)

Evaluate

4 y^{2} (9 y^{2} - 1)

Solution

4 y^{2} (3 y - 1) (3 y + 1)

Show Solution

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

Alternative Form

y_{1} = - 0. \dot{3}, y_{2} = 0, y_{3} = 0. \dot{3}

Evaluate

4 y^{2} (9 y^{2} - 1)

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

4 y^{2} (9 y^{2} - 1) = 0

Elimination the left coefficient

y^{2} (9 y^{2} - 1) = 0

Separate the equation into 2 possible cases

y^{2} = 0 9 y^{2} - 1 = 0

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

y = 0 9 y^{2} - 1 = 0

Solve the equation

More Steps

Evaluate

9 y^{2} - 1 = 0

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

9 y^{2} = 0 + 1

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

9 y^{2} = 1

Divide both sides

\frac{9 y ^{2}}{9} = \frac{1}{9}

Divide the numbers

y^{2} = \frac{1}{9}

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

y = \pm \frac{1}{9}

Simplify the expression

More Steps

Evaluate

\frac{1}{9}

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

\frac{1}{9}

Simplify the radical expression

\frac{1}{9}

Simplify the radical expression

\frac{1}{3}

y = \pm \frac{1}{3}

Separate the equation into 2 possible cases

y = \frac{1}{3} y = - \frac{1}{3}

y = 0 y = \frac{1}{3} y = - \frac{1}{3}

Solution

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

Alternative Form

y_{1} = - 0. \dot{3}, y_{2} = 0, y_{3} = 0. \dot{3}

Show Solution