Solve 37u^33u^3-40u^3

Question

Simplify the expression

111 u^{6} - 40 u^{3}

Evaluate

37 u^{3} \times 3 u^{3} - 40 u^{3}

Solution

More Steps

Evaluate

37 u^{3} \times 3 u^{3}

Multiply the terms

111 u^{3} \times u^{3}

Multiply the terms with the same base by adding their exponents

111 u^{3 + 3}

Add the numbers

111 u^{6}

111 u^{6} - 40 u^{3}

Show Solution

Factor the expression

u^{3} (111 u^{3} - 40)

Evaluate

37 u^{3} \times 3 u^{3} - 40 u^{3}

Multiply

More Steps

Evaluate

37 u^{3} \times 3 u^{3}

Multiply the terms

111 u^{3} \times u^{3}

Multiply the terms with the same base by adding their exponents

111 u^{3 + 3}

Add the numbers

111 u^{6}

111 u^{6} - 40 u^{3}

Rewrite the expression

u^{3} \times 111 u^{3} - u^{3} \times 40

Solution

u^{3} (111 u^{3} - 40)

Show Solution

Find the roots

u_{1} = 0, u_{2} = \frac{2 3 61605}{111}

Alternative Form

u_{1} = 0, u_{2} \approx 0.711616

Evaluate

37 u^{3} \times 3 u^{3} - 40 u^{3}

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

37 u^{3} \times 3 u^{3} - 40 u^{3} = 0

Multiply

More Steps

Multiply the terms

37 u^{3} \times 3 u^{3}

Multiply the terms

111 u^{3} \times u^{3}

Multiply the terms with the same base by adding their exponents

111 u^{3 + 3}

Add the numbers

111 u^{6}

111 u^{6} - 40 u^{3} = 0

Factor the expression

u^{3} (111 u^{3} - 40) = 0

Separate the equation into 2 possible cases

u^{3} = 0 111 u^{3} - 40 = 0

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

u = 0 111 u^{3} - 40 = 0

Solve the equation

More Steps

Evaluate

111 u^{3} - 40 = 0

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

111 u^{3} = 0 + 40

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

111 u^{3} = 40

Divide both sides

\frac{111 u ^{3}}{111} = \frac{40}{111}

Divide the numbers

u^{3} = \frac{40}{111}

Take the 3 -th root on both sides of the equation

3 u^{3} = 3 \frac{40}{111}

Calculate

u = 3 \frac{40}{111}

Simplify the root

More Steps

Evaluate

3 \frac{40}{111}

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

\frac{3 40}{3 111}

Simplify the radical expression

\frac{2 3 5}{3 111}

Multiply by the Conjugate

\frac{2 3 5 \times 3 11 1 ^{2}}{3 111 \times 3 11 1 ^{2}}

Simplify

\frac{2 3 5 \times 3 12321}{3 111 \times 3 11 1 ^{2}}

Multiply the numbers

\frac{2 3 61605}{3 111 \times 3 11 1 ^{2}}

Multiply the numbers

\frac{2 3 61605}{111}

u = \frac{2 3 61605}{111}

u = 0 u = \frac{2 3 61605}{111}

Solution

u_{1} = 0, u_{2} = \frac{2 3 61605}{111}

Alternative Form

u_{1} = 0, u_{2} \approx 0.711616

Show Solution