Solve (2x^3 - 3x^2) - (2x^2 - 3x^3)

Question

Simplify the expression

5 x^{3} - 5 x^{2}

Evaluate

(2 x^{3} - 3 x^{2}) - (2 x^{2} - 3 x^{3})

Remove the parentheses

2 x^{3} - 3 x^{2} - (2 x^{2} - 3 x^{3})

If a negative sign or a subtraction symbol appears outside parentheses, remove the parentheses and change the sign of every term within the parentheses

2 x^{3} - 3 x^{2} - 2 x^{2} + 3 x^{3}

Add the terms

More Steps

Evaluate

2 x^{3} + 3 x^{3}

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

(2 + 3) x^{3}

Add the numbers

5 x^{3}

5 x^{3} - 3 x^{2} - 2 x^{2}

Solution

More Steps

Evaluate

- 3 x^{2} - 2 x^{2}

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

(- 3 - 2) x^{2}

Subtract the numbers

- 5 x^{2}

5 x^{3} - 5 x^{2}

Show Solution

Factor the expression

5 x^{2} (x - 1)

Evaluate

(2 x^{3} - 3 x^{2}) - (2 x^{2} - 3 x^{3})

Remove the parentheses

2 x^{3} - 3 x^{2} - (2 x^{2} - 3 x^{3})

If a negative sign or a subtraction symbol appears outside parentheses, remove the parentheses and change the sign of every term within the parentheses

2 x^{3} - 3 x^{2} - 2 x^{2} + 3 x^{3}

Add the terms

More Steps

Evaluate

2 x^{3} + 3 x^{3}

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

(2 + 3) x^{3}

Add the numbers

5 x^{3}

5 x^{3} - 3 x^{2} - 2 x^{2}

Subtract the terms

More Steps

Evaluate

- 3 x^{2} - 2 x^{2}

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

(- 3 - 2) x^{2}

Subtract the numbers

- 5 x^{2}

5 x^{3} - 5 x^{2}

Rewrite the expression

5 x^{2} \times x - 5 x^{2}

Solution

5 x^{2} (x - 1)

Show Solution

Find the roots

x_{1} = 0, x_{2} = 1

Evaluate

(2 x^{3} - 3 x^{2}) - (2 x^{2} - 3 x^{3})

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

(2 x^{3} - 3 x^{2}) - (2 x^{2} - 3 x^{3}) = 0

Remove the parentheses

2 x^{3} - 3 x^{2} - (2 x^{2} - 3 x^{3}) = 0

Subtract the terms

More Steps

Simplify

2 x^{3} - 3 x^{2} - (2 x^{2} - 3 x^{3})

If a negative sign or a subtraction symbol appears outside parentheses, remove the parentheses and change the sign of every term within the parentheses

2 x^{3} - 3 x^{2} - 2 x^{2} + 3 x^{3}

Add the terms

More Steps

Evaluate

2 x^{3} + 3 x^{3}

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

(2 + 3) x^{3}

Add the numbers

5 x^{3}

5 x^{3} - 3 x^{2} - 2 x^{2}

Subtract the terms

More Steps

Evaluate

- 3 x^{2} - 2 x^{2}

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

(- 3 - 2) x^{2}

Subtract the numbers

- 5 x^{2}

5 x^{3} - 5 x^{2}

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

Factor the expression

5 x^{2} (x - 1) = 0

Divide both sides

x^{2} (x - 1) = 0

Separate the equation into 2 possible cases

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

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

x = 0 x - 1 = 0

Solve the equation

More Steps

Evaluate

x - 1 = 0

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

x = 0 + 1

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

x = 1

x = 0 x = 1

Solution

x_{1} = 0, x_{2} = 1

Show Solution