Solve 1/3(1-y) 2/3(1-y)

Question

Simplify the expression

\frac{2}{9} - \frac{4}{9} y + \frac{2}{9} y^{2}

Evaluate

\frac{1}{3} (1 - y) \times \frac{2}{3} (1 - y)

Multiply the terms

More Steps

Evaluate

\frac{1}{3} \times \frac{2}{3}

To multiply the fractions,multiply the numerators and denominators separately

\frac{2}{3 \times 3}

Multiply the numbers

\frac{2}{9}

\frac{2}{9} (1 - y) (1 - y)

Multiply the first two terms

More Steps

Evaluate

\frac{2}{9} (1 - y)

Apply the distributive property

\frac{2}{9} \times 1 - \frac{2}{9} y

Any expression multiplied by 1 remains the same

\frac{2}{9} - \frac{2}{9} y

(\frac{2}{9} - \frac{2}{9} y) (1 - y)

Apply the distributive property

\frac{2}{9} \times 1 - \frac{2}{9} y - \frac{2}{9} y \times 1 - (- \frac{2}{9} y \times y)

Any expression multiplied by 1 remains the same

\frac{2}{9} - \frac{2}{9} y - \frac{2}{9} y \times 1 - (- \frac{2}{9} y \times y)

Any expression multiplied by 1 remains the same

\frac{2}{9} - \frac{2}{9} y - \frac{2}{9} y - (- \frac{2}{9} y \times y)

Multiply the terms

\frac{2}{9} - \frac{2}{9} y - \frac{2}{9} y - (- \frac{2}{9} y^{2})

If a negative sign or a subtraction symbol appears outside parentheses, remove the parentheses and change the sign of every term within the parentheses

\frac{2}{9} - \frac{2}{9} y - \frac{2}{9} y + \frac{2}{9} y^{2}

Solution

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Evaluate

- \frac{2}{9} y - \frac{2}{9} y

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

(- \frac{2}{9} - \frac{2}{9}) y

Subtract the numbers

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Evaluate

- \frac{2}{9} - \frac{2}{9}

Write all numerators above the common denominator

\frac{- 2 - 2}{9}

Subtract the numbers

\frac{- 4}{9}

Use \frac{- a}{b} = \frac{a}{- b} = - \frac{a}{b} to rewrite the fraction

- \frac{4}{9}

- \frac{4}{9} y

\frac{2}{9} - \frac{4}{9} y + \frac{2}{9} y^{2}

Show Solution

Find the roots

y = 1

Evaluate

\frac{1}{3} (1 - y) \times \frac{2}{3} (1 - y)

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

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

Multiply the terms

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Multiply the terms

\frac{1}{3} (1 - y) \times \frac{2}{3} (1 - y)

Multiply the terms

More Steps

Evaluate

\frac{1}{3} \times \frac{2}{3}

To multiply the fractions,multiply the numerators and denominators separately

\frac{2}{3 \times 3}

Multiply the numbers

\frac{2}{9}

\frac{2}{9} (1 - y) (1 - y)

Multiply the first two terms

More Steps

Evaluate

\frac{2}{9} (1 - y)

Apply the distributive property

\frac{2}{9} \times 1 - \frac{2}{9} y

Any expression multiplied by 1 remains the same

\frac{2}{9} - \frac{2}{9} y

(\frac{2}{9} - \frac{2}{9} y) (1 - y)

(\frac{2}{9} - \frac{2}{9} y) (1 - y) = 0

Separate the equation into 2 possible cases

\frac{2}{9} - \frac{2}{9} y = 0 1 - y = 0

Solve the equation

More Steps

Evaluate

\frac{2}{9} - \frac{2}{9} y = 0

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

- \frac{2}{9} y = 0 - \frac{2}{9}

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

- \frac{2}{9} y = - \frac{2}{9}

Change the signs on both sides of the equation

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

Multiply by the reciprocal

\frac{2}{9} y \times \frac{9}{2} = \frac{2}{9} \times \frac{9}{2}

Multiply

y = \frac{2}{9} \times \frac{9}{2}

Multiply

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Evaluate

\frac{2}{9} \times \frac{9}{2}

Reduce the numbers

\frac{1}{9} \times 9

Reduce the numbers

1 \times 1

Simplify

1

y = 1

y = 1 1 - y = 0

Solve the equation

More Steps

Evaluate

1 - y = 0

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

- y = 0 - 1

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

- y = - 1

Change the signs on both sides of the equation

y = 1

y = 1 y = 1

Solution

y = 1

Show Solution