Solve 3y^2y-3y - ScanMath

Question

Simplify the expression

3 y^{3} - 3 y

Evaluate

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

Solution

More Steps

Evaluate

3 y^{2} \times y

Multiply the terms with the same base by adding their exponents

3 y^{2 + 1}

Add the numbers

3 y^{3}

3 y^{3} - 3 y

Show Solution

3 y (y - 1) (y + 1)

Evaluate

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

Evaluate

More Steps

Evaluate

3 y^{2} \times y

Multiply the terms with the same base by adding their exponents

3 y^{2 + 1}

Add the numbers

3 y^{3}

3 y^{3} - 3 y

Factor out 3 y from the expression

3 y (y^{2} - 1)

Solution

More Steps

Evaluate

y^{2} - 1

Rewrite the expression in exponential form

y^{2} - 1^{2}

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

(y - 1) (y + 1)

3 y (y - 1) (y + 1)

Show Solution

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

Evaluate

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

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

3 y^{2} \times y - 3 y = 0

Multiply

More Steps

Multiply the terms

3 y^{2} \times y

Multiply the terms with the same base by adding their exponents

3 y^{2 + 1}

Add the numbers

3 y^{3}

3 y^{3} - 3 y = 0

Factor the expression

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

Divide both sides

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

Separate the equation into 2 possible cases

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

Solve the equation

More Steps

Evaluate

y^{2} - 1 = 0

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

y^{2} = 0 + 1

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

y^{2} = 1

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

y = \pm 1

Simplify the expression

y = \pm 1

Separate the equation into 2 possible cases

y = 1 y = - 1

y = 0 y = 1 y = - 1

Solution

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

Show Solution