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

Question

Simplify the expression

2 x^{5} - 4 x^{4}

Evaluate

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

Remove the parentheses

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

Multiply the terms with the same base by adding their exponents

(x - 2) x^{2 + 2} \times 2

Add the numbers

(x - 2) x^{4} \times 2

Use the commutative property to reorder the terms

(x - 2) \times 2 x^{4}

Multiply the terms

2 x^{4} (x - 2)

Apply the distributive property

2 x^{4} \times x - 2 x^{4} \times 2

Multiply the terms

More Steps

Evaluate

x^{4} \times x

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

x^{4 + 1}

Add the numbers

x^{5}

2 x^{5} - 2 x^{4} \times 2

Solution

2 x^{5} - 4 x^{4}

Show Solution

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

Evaluate

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

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

(x - 2) (x^{2} \times 2 x^{2}) = 0

Multiply

More Steps

Multiply the terms

x^{2} \times 2 x^{2}

Multiply the terms with the same base by adding their exponents

x^{2 + 2} \times 2

Add the numbers

x^{4} \times 2

Use the commutative property to reorder the terms

2 x^{4}

(x - 2) \times 2 x^{4} = 0

Multiply the terms

2 x^{4} (x - 2) = 0

Elimination the left coefficient

x^{4} (x - 2) = 0

Separate the equation into 2 possible cases

x^{4} = 0 x - 2 = 0

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

x = 0 x - 2 = 0

Solve the equation

More Steps

Evaluate

x - 2 = 0

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

x = 0 + 2

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

x = 2

x = 0 x = 2

Solution

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

Show Solution