Solve (y^4 2)(3y^2-1)

Question

Simplify the expression

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

Evaluate

(y^{4} \times 2) (3 y^{2} - 1)

Remove the parentheses

y^{4} \times 2 (3 y^{2} - 1)

Use the commutative property to reorder the terms

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

Apply the distributive property

2 y^{4} \times 3 y^{2} - 2 y^{4} \times 1

Multiply the terms

More Steps

Evaluate

2 y^{4} \times 3 y^{2}

Multiply the numbers

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

Multiply the terms

More Steps

Evaluate

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

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

y^{4 + 2}

Add the numbers

y^{6}

6 y^{6}

6 y^{6} - 2 y^{4} \times 1

Solution

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

Show Solution

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

Alternative Form

y_{1} \approx - 0.57735, y_{2} = 0, y_{3} \approx 0.57735

Evaluate

(y^{4} \times 2) (3 y^{2} - 1)

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

(y^{4} \times 2) (3 y^{2} - 1) = 0

Use the commutative property to reorder the terms

2 y^{4} (3 y^{2} - 1) = 0

Elimination the left coefficient

y^{4} (3 y^{2} - 1) = 0

Separate the equation into 2 possible cases

y^{4} = 0 3 y^{2} - 1 = 0

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

y = 0 3 y^{2} - 1 = 0

Solve the equation

More Steps

Evaluate

3 y^{2} - 1 = 0

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

3 y^{2} = 0 + 1

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

3 y^{2} = 1

Divide both sides

\frac{3 y ^{2}}{3} = \frac{1}{3}

Divide the numbers

y^{2} = \frac{1}{3}

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

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

Simplify the expression

More Steps

Evaluate

\frac{1}{3}

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

\frac{1}{3}

Simplify the radical expression

\frac{1}{3}

Multiply by the Conjugate

\frac{3}{3 \times 3}

When a square root of an expression is multiplied by itself,the result is that expression

\frac{3}{3}

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

Separate the equation into 2 possible cases

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

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

Solution

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

Alternative Form

y_{1} \approx - 0.57735, y_{2} = 0, y_{3} \approx 0.57735

Show Solution