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

Question

Simplify the expression

3 y^{4} - 4 y^{3}

Evaluate

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

Remove the parentheses

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

Rewrite the expression

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

Multiply the terms with the same base by adding their exponents

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

Add the numbers

(3 y - 4) y^{3}

Multiply the terms

y^{3} (3 y - 4)

Apply the distributive property

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

Multiply the terms

More Steps

Evaluate

y^{3} \times 3 y

Use the commutative property to reorder the terms

3 y^{3} \times y

Multiply the terms

More Steps

Evaluate

y^{3} \times y

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

y^{3 + 1}

Add the numbers

y^{4}

3 y^{4}

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

Solution

3 y^{4} - 4 y^{3}

Show Solution

y_{1} = 0, y_{2} = \frac{4}{3}

Alternative Form

y_{1} = 0, y_{2} = 1. \dot{3}

Evaluate

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

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

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

Calculate

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

Any expression multiplied by 1 remains the same

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

Multiply the terms

More Steps

Multiply the terms

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

Multiply the terms with the same base by adding their exponents

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

Add the numbers

(3 y - 4) y^{3}

Multiply the terms

y^{3} (3 y - 4)

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

Separate the equation into 2 possible cases

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

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

y = 0 3 y - 4 = 0

Solve the equation

More Steps

Evaluate

3 y - 4 = 0

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

3 y = 0 + 4

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

3 y = 4

Divide both sides

\frac{3 y}{3} = \frac{4}{3}

Divide the numbers

y = \frac{4}{3}

y = 0 y = \frac{4}{3}

Solution

y_{1} = 0, y_{2} = \frac{4}{3}

Alternative Form

y_{1} = 0, y_{2} = 1. \dot{3}

Show Solution