Solve (m^2 m 1)(m^2-m 1)

Question

Simplify the expression

m^{5} - m^{4}

Evaluate

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

Remove the parentheses

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

Any expression multiplied by 1 remains the same

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

Rewrite the expression

m^{2} \times m (m^{2} - m)

Multiply the terms with the same base by adding their exponents

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

Add the numbers

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

Apply the distributive property

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

Multiply the terms

More Steps

Evaluate

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

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

m^{3 + 2}

Add the numbers

m^{5}

m^{5} - m^{3} \times m

Solution

More Steps

Evaluate

m^{3} \times m

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

m^{3 + 1}

Add the numbers

m^{4}

m^{5} - m^{4}

Show Solution

Factor the expression

m^{4} (m - 1)

Evaluate

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

Remove the parentheses

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

Any expression multiplied by 1 remains the same

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

Multiply the terms

More Steps

Multiply the terms

m^{2} \times m \times 1

Rewrite the expression

m^{2} \times m

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

m^{2 + 1}

Add the numbers

m^{3}

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

Factor the expression

More Steps

Evaluate

m^{2} - m

Rewrite the expression

m \times m - m

Factor out m from the expression

m (m - 1)

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

Solution

m^{4} (m - 1)

Show Solution

Find the roots

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

Evaluate

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

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

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

Multiply the terms

More Steps

Multiply the terms

m^{2} \times m \times 1

Rewrite the expression

m^{2} \times m

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

m^{2 + 1}

Add the numbers

m^{3}

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

Any expression multiplied by 1 remains the same

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

Separate the equation into 2 possible cases

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

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

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

Solve the equation

More Steps

Evaluate

m^{2} - m = 0

Factor the expression

More Steps

Evaluate

m^{2} - m

Rewrite the expression

m \times m - m

Factor out m from the expression

m (m - 1)

m (m - 1) = 0

When the product of factors equals 0,at least one factor is 0

m = 0 m - 1 = 0

Solve the equation for m

More Steps

Evaluate

m - 1 = 0

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

m = 0 + 1

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

m = 1

m = 0 m = 1

m = 0 m = 0 m = 1

Find the union

m = 0 m = 1

Solution

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

Show Solution