Solve m^3 2m^2-2m^3

Question

Simplify the expression

2 m^{5} - 2 m^{3}

Evaluate

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

Solution

More Steps

Evaluate

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

Multiply the terms with the same base by adding their exponents

m^{3 + 2} \times 2

Add the numbers

m^{5} \times 2

Use the commutative property to reorder the terms

2 m^{5}

2 m^{5} - 2 m^{3}

Show Solution

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

Evaluate

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

Evaluate

More Steps

Evaluate

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

Multiply the terms with the same base by adding their exponents

m^{3 + 2} \times 2

Add the numbers

m^{5} \times 2

Use the commutative property to reorder the terms

2 m^{5}

2 m^{5} - 2 m^{3}

Factor out 2 m^{3} from the expression

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

Solution

More Steps

Evaluate

m^{2} - 1

Rewrite the expression in exponential form

m^{2} - 1^{2}

Use a^{2} - b^{2} = (a - b) (a + b) to factor the expression

(m - 1) (m + 1)

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

Show Solution

m_{1} = - 1, m_{2} = 0, m_{3} = 1

Evaluate

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

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

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

Multiply

More Steps

Multiply the terms

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

Multiply the terms with the same base by adding their exponents

m^{3 + 2} \times 2

Add the numbers

m^{5} \times 2

Use the commutative property to reorder the terms

2 m^{5}

2 m^{5} - 2 m^{3} = 0

Factor the expression

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

Divide both sides

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

Separate the equation into 2 possible cases

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

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

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

Solve the equation

More Steps

Evaluate

m^{2} - 1 = 0

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

m^{2} = 0 + 1

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

m^{2} = 1

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

m = \pm 1

Simplify the expression

m = \pm 1

Separate the equation into 2 possible cases

m = 1 m = - 1

m = 0 m = 1 m = - 1

Solution

m_{1} = - 1, m_{2} = 0, m_{3} = 1

Show Solution