Solve (2m^2 3m - 1) (4m^2 - 5m^2)

Question

Simplify the expression

- 6 m^{5} + m^{2}

Evaluate

(2 m^{2} \times 3 m - 1) (4 m^{2} - 5 m^{2})

Multiply

More Steps

Multiply the terms

2 m^{2} \times 3 m

Multiply the terms

6 m^{2} \times m

Multiply the terms with the same base by adding their exponents

6 m^{2 + 1}

Add the numbers

6 m^{3}

(6 m^{3} - 1) (4 m^{2} - 5 m^{2})

Subtract the terms

More Steps

Simplify

4 m^{2} - 5 m^{2}

Collect like terms by calculating the sum or difference of their coefficients

(4 - 5) m^{2}

Subtract the numbers

- m^{2}

(6 m^{3} - 1) (- m^{2})

Multiply the terms

- m^{2} (6 m^{3} - 1)

Apply the distributive property

- m^{2} \times 6 m^{3} - (- m^{2} \times 1)

Multiply the terms

More Steps

Evaluate

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

Multiply the numbers

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

Multiply the terms

More Steps

Evaluate

m^{2} \times m^{3}

Use the product rule a^{n} \times a^{m} = a^{n + m} to simplify the expression

m^{2 + 3}

Add the numbers

m^{5}

- 6 m^{5}

- 6 m^{5} - (- m^{2} \times 1)

Any expression multiplied by 1 remains the same

- 6 m^{5} - (- m^{2})

Solution

- 6 m^{5} + m^{2}

Show Solution

Find the roots

m_{1} = 0, m_{2} = \frac{3 36}{6}

Alternative Form

m_{1} = 0, m_{2} \approx 0.550321

Evaluate

(2 m^{2} \times 3 m - 1) (4 m^{2} - 5 m^{2})

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

(2 m^{2} \times 3 m - 1) (4 m^{2} - 5 m^{2}) = 0

Multiply

More Steps

Multiply the terms

2 m^{2} \times 3 m

Multiply the terms

6 m^{2} \times m

Multiply the terms with the same base by adding their exponents

6 m^{2 + 1}

Add the numbers

6 m^{3}

(6 m^{3} - 1) (4 m^{2} - 5 m^{2}) = 0

Subtract the terms

More Steps

Simplify

4 m^{2} - 5 m^{2}

Collect like terms by calculating the sum or difference of their coefficients

(4 - 5) m^{2}

Subtract the numbers

- m^{2}

(6 m^{3} - 1) (- m^{2}) = 0

Multiply the terms

- m^{2} (6 m^{3} - 1) = 0

Change the sign

m^{2} (6 m^{3} - 1) = 0

Separate the equation into 2 possible cases

m^{2} = 0 6 m^{3} - 1 = 0

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

m = 0 6 m^{3} - 1 = 0

Solve the equation

More Steps

Evaluate

6 m^{3} - 1 = 0

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

6 m^{3} = 0 + 1

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

6 m^{3} = 1

Divide both sides

\frac{6 m ^{3}}{6} = \frac{1}{6}

Divide the numbers

m^{3} = \frac{1}{6}

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

3 m^{3} = 3 \frac{1}{6}

Calculate

m = 3 \frac{1}{6}

Simplify the root

More Steps

Evaluate

3 \frac{1}{6}

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

\frac{3 1}{3 6}

Simplify the radical expression

\frac{1}{3 6}

Multiply by the Conjugate

\frac{3 6 ^{2}}{3 6 \times 3 6 ^{2}}

Simplify

\frac{3 36}{3 6 \times 3 6 ^{2}}

Multiply the numbers

\frac{3 36}{6}

m = \frac{3 36}{6}

m = 0 m = \frac{3 36}{6}

Solution

m_{1} = 0, m_{2} = \frac{3 36}{6}

Alternative Form

m_{1} = 0, m_{2} \approx 0.550321

Show Solution