Solve 10y^4y 8y-4y

Question

Simplify the expression

80 y^{6} - 4 y

Evaluate

10 y^{4} \times y \times 8 y - 4 y

Solution

More Steps

Evaluate

10 y^{4} \times y \times 8 y

Multiply the terms

80 y^{4} \times y \times y

Multiply the terms with the same base by adding their exponents

80 y^{4 + 1 + 1}

Add the numbers

80 y^{6}

80 y^{6} - 4 y

Show Solution

Factor the expression

4 y (20 y^{5} - 1)

Evaluate

10 y^{4} \times y \times 8 y - 4 y

Multiply

More Steps

Evaluate

10 y^{4} \times y \times 8 y

Multiply the terms

80 y^{4} \times y \times y

Multiply the terms with the same base by adding their exponents

80 y^{4 + 1 + 1}

Add the numbers

80 y^{6}

80 y^{6} - 4 y

Rewrite the expression

4 y \times 20 y^{5} - 4 y

Solution

4 y (20 y^{5} - 1)

Show Solution

Find the roots

y_{1} = 0, y_{2} = \frac{5 2 0 ^{4}}{20}

Alternative Form

y_{1} = 0, y_{2} \approx 0.54928

Evaluate

10 y^{4} \times y \times 8 y - 4 y

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

10 y^{4} \times y \times 8 y - 4 y = 0

Multiply

More Steps

Multiply the terms

10 y^{4} \times y \times 8 y

Multiply the terms

80 y^{4} \times y \times y

Multiply the terms with the same base by adding their exponents

80 y^{4 + 1 + 1}

Add the numbers

80 y^{6}

80 y^{6} - 4 y = 0

Factor the expression

4 y (20 y^{5} - 1) = 0

Divide both sides

y (20 y^{5} - 1) = 0

Separate the equation into 2 possible cases

y = 0 20 y^{5} - 1 = 0

Solve the equation

More Steps

Evaluate

20 y^{5} - 1 = 0

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

20 y^{5} = 0 + 1

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

20 y^{5} = 1

Divide both sides

\frac{20 y ^{5}}{20} = \frac{1}{20}

Divide the numbers

y^{5} = \frac{1}{20}

Take the 5 -th root on both sides of the equation

5 y^{5} = 5 \frac{1}{20}

Calculate

y = 5 \frac{1}{20}

Simplify the root

More Steps

Evaluate

5 \frac{1}{20}

To take a root of a fraction,take the root of the numerator and denominator separately

\frac{5 1}{5 20}

Simplify the radical expression

\frac{1}{5 20}

Multiply by the Conjugate

\frac{5 2 0 ^{4}}{5 20 \times 5 2 0 ^{4}}

Multiply the numbers

\frac{5 2 0 ^{4}}{20}

y = \frac{5 2 0 ^{4}}{20}

y = 0 y = \frac{5 2 0 ^{4}}{20}

Solution

y_{1} = 0, y_{2} = \frac{5 2 0 ^{4}}{20}

Alternative Form

y_{1} = 0, y_{2} \approx 0.54928

Show Solution