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

Question

Simplify the expression

16 x^{6} - 64 x^{5} + 64 x^{4}

Evaluate

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

Multiply the terms

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

Multiply the terms with the same base by adding their exponents

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

Add the numbers

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

Multiply the terms

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

Expand the expression

More Steps

Evaluate

(2 x - 4)^{2}

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

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

Calculate

4 x^{2} - 16 x + 16

4 x^{4} (4 x^{2} - 16 x + 16)

Apply the distributive property

4 x^{4} \times 4 x^{2} - 4 x^{4} \times 16 x + 4 x^{4} \times 16

Multiply the terms

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Evaluate

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

Multiply the numbers

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

Multiply the terms

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Evaluate

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

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

x^{4 + 2}

Add the numbers

x^{6}

16 x^{6}

16 x^{6} - 4 x^{4} \times 16 x + 4 x^{4} \times 16

Multiply the terms

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Evaluate

4 x^{4} \times 16 x

Multiply the numbers

64 x^{4} \times x

Multiply the terms

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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}

64 x^{5}

16 x^{6} - 64 x^{5} + 4 x^{4} \times 16

Solution

16 x^{6} - 64 x^{5} + 64 x^{4}

Show Solution

Factor the expression

16 x^{4} (x - 2)^{2}

Evaluate

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

Multiply the terms

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

Multiply the terms with the same base by adding their exponents

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

Add the numbers

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

Multiply the terms

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

Factor the expression

More Steps

Evaluate

(2 x - 4)^{2}

Factor the expression

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

Evaluate the power

4 (x - 2)^{2}

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

Solution

16 x^{4} (x - 2)^{2}

Show Solution

Find the roots

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

Evaluate

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

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

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

Multiply the terms

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

Multiply the terms

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

Multiply the terms

More Steps

Multiply the terms

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

Multiply the terms

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

Multiply the terms with the same base by adding their exponents

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

Add the numbers

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

Multiply the terms

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

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

Elimination the left coefficient

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

Separate the equation into 2 possible cases

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

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

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

Solve the equation

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Evaluate

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

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

2 x - 4 = 0

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

2 x = 0 + 4

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

2 x = 4

Divide both sides

\frac{2 x}{2} = \frac{4}{2}

Divide the numbers

x = \frac{4}{2}

Divide the numbers

More Steps

Evaluate

\frac{4}{2}

Reduce the numbers

\frac{2}{1}

Calculate

2

x = 2

x = 0 x = 2

Solution

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

Show Solution