Solve (y-1)(3y-9)

Question

Simplify the expression

3 y^{2} - 12 y + 9

Evaluate

(y - 1) (3 y - 9)

Apply the distributive property

y \times 3 y - y \times 9 - 3 y - (- 9)

Multiply the terms

More Steps

Evaluate

y \times 3 y

Use the commutative property to reorder the terms

3 y \times y

Multiply the terms

3 y^{2}

3 y^{2} - y \times 9 - 3 y - (- 9)

Use the commutative property to reorder the terms

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

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

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

Solution

More Steps

Evaluate

- 9 y - 3 y

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

(- 9 - 3) y

Subtract the numbers

- 12 y

3 y^{2} - 12 y + 9

Show Solution

Factor the expression

3 (y - 1) (y - 3)

Evaluate

(y - 1) (3 y - 9)

Factor the expression

(y - 1) \times 3 (y - 3)

Solution

3 (y - 1) (y - 3)

Show Solution

Find the roots

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

Evaluate

(y - 1) (3 y - 9)

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

(y - 1) (3 y - 9) = 0

Separate the equation into 2 possible cases

y - 1 = 0 3 y - 9 = 0

Solve the equation

More Steps

Evaluate

y - 1 = 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

y = 1 3 y - 9 = 0

Solve the equation

More Steps

Evaluate

3 y - 9 = 0

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

3 y = 0 + 9

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

3 y = 9

Divide both sides

\frac{3 y}{3} = \frac{9}{3}

Divide the numbers

y = \frac{9}{3}

Divide the numbers

More Steps

Evaluate

\frac{9}{3}

Reduce the numbers

\frac{3}{1}

Calculate

3

y = 3

y = 1 y = 3

Solution

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

Show Solution