Solve m^4 - m^3 - 7m^2 3m

Question

Simplify the expression

m^{4} - 22 m^{3}

Evaluate

m^{4} - m^{3} - 7 m^{2} \times 3 m

Multiply

More Steps

Multiply the terms

- 7 m^{2} \times 3 m

Multiply the terms

- 21 m^{2} \times m

Multiply the terms with the same base by adding their exponents

- 21 m^{2 + 1}

Add the numbers

- 21 m^{3}

m^{4} - m^{3} - 21 m^{3}

Solution

More Steps

Evaluate

- m^{3} - 21 m^{3}

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

(- 1 - 21) m^{3}

Subtract the numbers

- 22 m^{3}

m^{4} - 22 m^{3}

Show Solution

Factor the expression

m^{3} (m - 22)

Evaluate

m^{4} - m^{3} - 7 m^{2} \times 3 m

Multiply

More Steps

Multiply the terms

7 m^{2} \times 3 m

Multiply the terms

21 m^{2} \times m

Multiply the terms with the same base by adding their exponents

21 m^{2 + 1}

Add the numbers

21 m^{3}

m^{4} - m^{3} - 21 m^{3}

Subtract the terms

More Steps

Evaluate

- m^{3} - 21 m^{3}

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

(- 1 - 21) m^{3}

Subtract the numbers

- 22 m^{3}

m^{4} - 22 m^{3}

Rewrite the expression

m^{3} \times m - m^{3} \times 22

Solution

m^{3} (m - 22)

Show Solution

Find the roots

m_{1} = 0, m_{2} = 22

Evaluate

m^{4} - m^{3} - 7 m^{2} \times 3 m

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

m^{4} - m^{3} - 7 m^{2} \times 3 m = 0

Multiply

More Steps

Multiply the terms

7 m^{2} \times 3 m

Multiply the terms

21 m^{2} \times m

Multiply the terms with the same base by adding their exponents

21 m^{2 + 1}

Add the numbers

21 m^{3}

m^{4} - m^{3} - 21 m^{3} = 0

Subtract the terms

More Steps

Simplify

m^{4} - m^{3} - 21 m^{3}

Subtract the terms

More Steps

Evaluate

- m^{3} - 21 m^{3}

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

(- 1 - 21) m^{3}

Subtract the numbers

- 22 m^{3}

m^{4} - 22 m^{3}

m^{4} - 22 m^{3} = 0

Factor the expression

m^{3} (m - 22) = 0

Separate the equation into 2 possible cases

m^{3} = 0 m - 22 = 0

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

m = 0 m - 22 = 0

Solve the equation

More Steps

Evaluate

m - 22 = 0

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

m = 0 + 22

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

m = 22

m = 0 m = 22

Solution

m_{1} = 0, m_{2} = 22

Show Solution