Solve 10y^3 40y^2 - 5y

Question

Simplify the expression

400 y^{5} - 5 y

Evaluate

10 y^{3} \times 40 y^{2} - 5 y

Solution

More Steps

Evaluate

10 y^{3} \times 40 y^{2}

Multiply the terms

400 y^{3} \times y^{2}

Multiply the terms with the same base by adding their exponents

400 y^{3 + 2}

Add the numbers

400 y^{5}

400 y^{5} - 5 y

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Factor the expression

5 y (80 y^{4} - 1)

Evaluate

10 y^{3} \times 40 y^{2} - 5 y

Multiply

More Steps

Evaluate

10 y^{3} \times 40 y^{2}

Multiply the terms

400 y^{3} \times y^{2}

Multiply the terms with the same base by adding their exponents

400 y^{3 + 2}

Add the numbers

400 y^{5}

400 y^{5} - 5 y

Rewrite the expression

5 y \times 80 y^{4} - 5 y

Solution

5 y (80 y^{4} - 1)

Show Solution

Find the roots

y_{1} = - \frac{4 125}{10}, y_{2} = 0, y_{3} = \frac{4 125}{10}

Alternative Form

y_{1} \approx - 0.33437, y_{2} = 0, y_{3} \approx 0.33437

Evaluate

10 y^{3} \times 40 y^{2} - 5 y

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

10 y^{3} \times 40 y^{2} - 5 y = 0

Multiply

More Steps

Multiply the terms

10 y^{3} \times 40 y^{2}

Multiply the terms

400 y^{3} \times y^{2}

Multiply the terms with the same base by adding their exponents

400 y^{3 + 2}

Add the numbers

400 y^{5}

400 y^{5} - 5 y = 0

Factor the expression

5 y (80 y^{4} - 1) = 0

Divide both sides

y (80 y^{4} - 1) = 0

Separate the equation into 2 possible cases

y = 0 80 y^{4} - 1 = 0

Solve the equation

More Steps

Evaluate

80 y^{4} - 1 = 0

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

80 y^{4} = 0 + 1

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

80 y^{4} = 1

Divide both sides

\frac{80 y ^{4}}{80} = \frac{1}{80}

Divide the numbers

y^{4} = \frac{1}{80}

Take the root of both sides of the equation and remember to use both positive and negative roots

y = \pm 4 \frac{1}{80}

Simplify the expression

More Steps

Evaluate

4 \frac{1}{80}

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

\frac{4 1}{4 80}

Simplify the radical expression

\frac{1}{4 80}

Simplify the radical expression

\frac{1}{2 4 5}

Multiply by the Conjugate

\frac{4 5 ^{3}}{2 4 5 \times 4 5 ^{3}}

Simplify

\frac{4 125}{2 4 5 \times 4 5 ^{3}}

Multiply the numbers

\frac{4 125}{10}

y = \pm \frac{4 125}{10}

Separate the equation into 2 possible cases

y = \frac{4 125}{10} y = - \frac{4 125}{10}

y = 0 y = \frac{4 125}{10} y = - \frac{4 125}{10}

Solution

y_{1} = - \frac{4 125}{10}, y_{2} = 0, y_{3} = \frac{4 125}{10}

Alternative Form

y_{1} \approx - 0.33437, y_{2} = 0, y_{3} \approx 0.33437

Show Solution