Solve 4(x-2) (x 1) 2 (x-2) (x 1)^2

Question

Simplify the expression

8 x^{5} - 32 x^{4} + 32 x^{3}

Evaluate

4 (x - 2) (x \times 1) \times 2 (x - 2) (x \times 1)^{2}

Remove the parentheses

4 (x - 2) x \times 1 \times 2 (x - 2) (x \times 1)^{2}

Any expression multiplied by 1 remains the same

4 (x - 2) x \times 1 \times 2 (x - 2) x^{2}

Rewrite the expression

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

Multiply the terms

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

Multiply the terms with the same base by adding their exponents

8 (x - 2) x^{1 + 2} (x - 2)

Add the numbers

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

Multiply the terms

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

Multiply the terms

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

Expand the expression

More Steps

Evaluate

(x - 2)^{2}

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

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

Calculate

x^{2} - 4 x + 4

8 x^{3} (x^{2} - 4 x + 4)

Apply the distributive property

8 x^{3} \times x^{2} - 8 x^{3} \times 4 x + 8 x^{3} \times 4

Multiply the terms

More Steps

Evaluate

x^{3} \times x^{2}

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

x^{3 + 2}

Add the numbers

x^{5}

8 x^{5} - 8 x^{3} \times 4 x + 8 x^{3} \times 4

Multiply the terms

More Steps

Evaluate

8 x^{3} \times 4 x

Multiply the numbers

32 x^{3} \times x

Multiply the terms

More Steps

Evaluate

x^{3} \times x

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

x^{3 + 1}

Add the numbers

x^{4}

32 x^{4}

8 x^{5} - 32 x^{4} + 8 x^{3} \times 4

Solution

8 x^{5} - 32 x^{4} + 32 x^{3}

Show Solution

Find the roots

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

Evaluate

4 (x - 2) (x \times 1) \times 2 (x - 2) (x \times 1)^{2}

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

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

Any expression multiplied by 1 remains the same

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

Any expression multiplied by 1 remains the same

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

Multiply the terms

More Steps

Multiply the terms

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

Multiply the terms

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

Multiply the terms with the same base by adding their exponents

8 (x - 2) x^{1 + 2} (x - 2)

Add the numbers

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

Multiply the terms

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

Multiply the terms

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

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

Elimination the left coefficient

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

Separate the equation into 2 possible cases

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

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

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

Solve the equation

More Steps

Evaluate

(x - 2)^{2} = 0

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

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