Solve 4m^2-3m^6 5m^4

Question

Simplify the expression

4 m^{2} - 15 m^{10}

Evaluate

4 m^{2} - 3 m^{6} \times 5 m^{4}

Solution

More Steps

Evaluate

3 m^{6} \times 5 m^{4}

Multiply the terms

15 m^{6} \times m^{4}

Multiply the terms with the same base by adding their exponents

15 m^{6 + 4}

Add the numbers

15 m^{10}

4 m^{2} - 15 m^{10}

Show Solution

Factor the expression

m^{2} (4 - 15 m^{8})

Evaluate

4 m^{2} - 3 m^{6} \times 5 m^{4}

Multiply

More Steps

Evaluate

3 m^{6} \times 5 m^{4}

Multiply the terms

15 m^{6} \times m^{4}

Multiply the terms with the same base by adding their exponents

15 m^{6 + 4}

Add the numbers

15 m^{10}

4 m^{2} - 15 m^{10}

Rewrite the expression

m^{2} \times 4 - m^{2} \times 15 m^{8}

Solution

m^{2} (4 - 15 m^{8})

Show Solution

Find the roots

m_{1} = - \frac{8 4 \times 1 5 ^{7}}{15}, m_{2} = 0, m_{3} = \frac{8 4 \times 1 5 ^{7}}{15}

Alternative Form

m_{1} \approx - 0.847708, m_{2} = 0, m_{3} \approx 0.847708

Evaluate

4 m^{2} - 3 m^{6} \times 5 m^{4}

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

4 m^{2} - 3 m^{6} \times 5 m^{4} = 0

Multiply

More Steps

Multiply the terms

3 m^{6} \times 5 m^{4}

Multiply the terms

15 m^{6} \times m^{4}

Multiply the terms with the same base by adding their exponents

15 m^{6 + 4}

Add the numbers

15 m^{10}

4 m^{2} - 15 m^{10} = 0

Factor the expression

m^{2} (4 - 15 m^{8}) = 0

Separate the equation into 2 possible cases

m^{2} = 0 4 - 15 m^{8} = 0

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

m = 0 4 - 15 m^{8} = 0

Solve the equation

More Steps

Evaluate

4 - 15 m^{8} = 0

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

- 15 m^{8} = 0 - 4

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

- 15 m^{8} = - 4

Change the signs on both sides of the equation

15 m^{8} = 4

Divide both sides

\frac{15 m ^{8}}{15} = \frac{4}{15}

Divide the numbers

m^{8} = \frac{4}{15}

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

m = \pm 8 \frac{4}{15}

Simplify the expression

More Steps

Evaluate

8 \frac{4}{15}

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

\frac{8 4}{8 15}

Simplify the radical expression

\frac{4 2}{8 15}

Multiply by the Conjugate

\frac{4 2 \times 8 1 5 ^{7}}{8 15 \times 8 1 5 ^{7}}

Multiply the numbers

\frac{8 4 \times 1 5 ^{7}}{8 15 \times 8 1 5 ^{7}}

Multiply the numbers

\frac{8 4 \times 1 5 ^{7}}{15}

m = \pm \frac{8 4 \times 1 5 ^{7}}{15}

Separate the equation into 2 possible cases

m = \frac{8 4 \times 1 5 ^{7}}{15} m = - \frac{8 4 \times 1 5 ^{7}}{15}

m = 0 m = \frac{8 4 \times 1 5 ^{7}}{15} m = - \frac{8 4 \times 1 5 ^{7}}{15}

Solution

m_{1} = - \frac{8 4 \times 1 5 ^{7}}{15}, m_{2} = 0, m_{3} = \frac{8 4 \times 1 5 ^{7}}{15}

Alternative Form

m_{1} \approx - 0.847708, m_{2} = 0, m_{3} \approx 0.847708

Show Solution