Solve 1-(3y-1)^3 - ScanMath

Question

Simplify the expression

2 - 27 y^{3} + 27 y^{2} - 9 y

Evaluate

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

Expand the expression

1 - 27 y^{3} + 27 y^{2} - 9 y + 1

Solution

2 - 27 y^{3} + 27 y^{2} - 9 y

Show Solution

(2 - 3 y) (- 3 y + 9 y^{2} + 1)

Evaluate

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

Rewrite the expression in exponential form

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

Use a^{3} - b^{3} = (a - b) (a^{2} + ab + b^{2}) to factor the expression

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

1 raised to any power equals to 1

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

Any expression multiplied by 1 remains the same

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

Factor the expression

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

Calculate

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

Solution

More Steps

Simplify

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

Since two opposites add up to 0,remove them form the expression

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

Expand the expression

3 y + 9 y^{2} - 6 y + 1

Subtract the terms

More Steps

Evaluate

3 y - 6 y

Collect like terms by calculating the sum or difference of their coefficients

(3 - 6) y

Subtract the numbers

- 3 y

- 3 y + 9 y^{2} + 1

(2 - 3 y) (- 3 y + 9 y^{2} + 1)

Show Solution

y = \frac{2}{3}

Alternative Form

y = 0. \dot{6}

Evaluate

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

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

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

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

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

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

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

Change the signs on both sides of the equation

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

Take the 3 -th root on both sides of the equation

3 (3 y - 1)^{3} = 31

Calculate

3 y - 1 = 31

Simplify the root

3 y - 1 = 1

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

3 y = 1 + 1

Add the numbers

3 y = 2

Divide both sides

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

Solution

y = \frac{2}{3}

Alternative Form

y = 0. \dot{6}

Show Solution