Solve (a^(3)-2a^(2))-(3a^(2)-4a^(2))

Question

Simplify the expression

a^{3} - a^{2}

Evaluate

(a^{3} - 2 a^{2}) - (3 a^{2} - 4 a^{2})

Remove the parentheses

a^{3} - 2 a^{2} - (3 a^{2} - 4 a^{2})

Subtract the terms

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Simplify

3 a^{2} - 4 a^{2}

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

(3 - 4) a^{2}

Subtract the numbers

- a^{2}

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

Rewrite the expression

a^{3} - 2 a^{2} + a^{2}

Solution

More Steps

Evaluate

- 2 a^{2} + a^{2}

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

(- 2 + 1) a^{2}

Add the numbers

- a^{2}

a^{3} - a^{2}

Show Solution

Factor the expression

a^{2} (a - 1)

Evaluate

(a^{3} - 2 a^{2}) - (3 a^{2} - 4 a^{2})

Remove the parentheses

a^{3} - 2 a^{2} - (3 a^{2} - 4 a^{2})

Subtract the terms

More Steps

Simplify

3 a^{2} - 4 a^{2}

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

(3 - 4) a^{2}

Subtract the numbers

- a^{2}

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

Rewrite the expression

a^{3} - 2 a^{2} + a^{2}

Add the terms

More Steps

Evaluate

- 2 a^{2} + a^{2}

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

(- 2 + 1) a^{2}

Add the numbers

- a^{2}

a^{3} - a^{2}

Rewrite the expression

a^{2} \times a - a^{2}

Solution

a^{2} (a - 1)

Show Solution

Find the roots

a_{1} = 0, a_{2} = 1

Evaluate

(a^{3} - 2 a^{2}) - (3 a^{2} - 4 a^{2})

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

(a^{3} - 2 a^{2}) - (3 a^{2} - 4 a^{2}) = 0

Remove the parentheses

a^{3} - 2 a^{2} - (3 a^{2} - 4 a^{2}) = 0

Subtract the terms

More Steps

Simplify

3 a^{2} - 4 a^{2}

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

(3 - 4) a^{2}

Subtract the numbers

- a^{2}

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

Subtract the terms

More Steps

Simplify

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

Rewrite the expression

a^{3} - 2 a^{2} + a^{2}

Add the terms

More Steps

Evaluate

- 2 a^{2} + a^{2}

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

(- 2 + 1) a^{2}

Add the numbers

- a^{2}

a^{3} - a^{2}

a^{3} - a^{2} = 0

Factor the expression

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

Separate the equation into 2 possible cases

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

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

a = 0 a - 1 = 0

Solve the equation

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Evaluate

a - 1 = 0

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

a = 0 + 1

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

a = 1

a = 0 a = 1

Solution

a_{1} = 0, a_{2} = 1

Show Solution