Solve (5u^26u^5)-(4u^3)

Question

Simplify the expression

30 u^{7} - 4 u^{3}

Evaluate

(5 u^{2} \times 6 u^{5}) - 4 u^{3}

Solution

More Steps

Evaluate

5 u^{2} \times 6 u^{5}

Multiply the terms

30 u^{2} \times u^{5}

Multiply the terms with the same base by adding their exponents

30 u^{2 + 5}

Add the numbers

30 u^{7}

30 u^{7} - 4 u^{3}

Show Solution

Factor the expression

2 u^{3} (15 u^{4} - 2)

Evaluate

(5 u^{2} \times 6 u^{5}) - 4 u^{3}

Multiply

More Steps

Evaluate

5 u^{2} \times 6 u^{5}

Multiply the terms

30 u^{2} \times u^{5}

Multiply the terms with the same base by adding their exponents

30 u^{2 + 5}

Add the numbers

30 u^{7}

30 u^{7} - 4 u^{3}

Rewrite the expression

2 u^{3} \times 15 u^{4} - 2 u^{3} \times 2

Solution

2 u^{3} (15 u^{4} - 2)

Show Solution

Find the roots

u_{1} = - \frac{4 6750}{15}, u_{2} = 0, u_{3} = \frac{4 6750}{15}

Alternative Form

u_{1} \approx - 0.604275, u_{2} = 0, u_{3} \approx 0.604275

Evaluate

(5 u^{2} \times 6 u^{5}) - (4 u^{3})

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

(5 u^{2} \times 6 u^{5}) - (4 u^{3}) = 0

Multiply

More Steps

Multiply the terms

5 u^{2} \times 6 u^{5}

Multiply the terms

30 u^{2} \times u^{5}

Multiply the terms with the same base by adding their exponents

30 u^{2 + 5}

Add the numbers

30 u^{7}

30 u^{7} - (4 u^{3}) = 0

Multiply the terms

30 u^{7} - 4 u^{3} = 0

Factor the expression

2 u^{3} (15 u^{4} - 2) = 0

Divide both sides

u^{3} (15 u^{4} - 2) = 0

Separate the equation into 2 possible cases

u^{3} = 0 15 u^{4} - 2 = 0

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

u = 0 15 u^{4} - 2 = 0

Solve the equation

More Steps

Evaluate

15 u^{4} - 2 = 0

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

15 u^{4} = 0 + 2

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

15 u^{4} = 2

Divide both sides

\frac{15 u ^{4}}{15} = \frac{2}{15}

Divide the numbers

u^{4} = \frac{2}{15}

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

u = \pm 4 \frac{2}{15}

Simplify the expression

More Steps

Evaluate

4 \frac{2}{15}

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

\frac{4 2}{4 15}

Multiply by the Conjugate

\frac{4 2 \times 4 1 5 ^{3}}{4 15 \times 4 1 5 ^{3}}

Simplify

\frac{4 2 \times 4 3375}{4 15 \times 4 1 5 ^{3}}

Multiply the numbers

\frac{4 6750}{4 15 \times 4 1 5 ^{3}}

Multiply the numbers

\frac{4 6750}{15}

u = \pm \frac{4 6750}{15}

Separate the equation into 2 possible cases

u = \frac{4 6750}{15} u = - \frac{4 6750}{15}

u = 0 u = \frac{4 6750}{15} u = - \frac{4 6750}{15}

Solution

u_{1} = - \frac{4 6750}{15}, u_{2} = 0, u_{3} = \frac{4 6750}{15}

Alternative Form

u_{1} \approx - 0.604275, u_{2} = 0, u_{3} \approx 0.604275

Show Solution