Solve (x^5)2(x 1)(2x-4)

Question

Simplify the expression

4 x^{7} - 8 x^{6}

Evaluate

x^{5} \times 2 (x \times 1) (2 x - 4)

Remove the parentheses

x^{5} \times 2 x \times 1 \times (2 x - 4)

Rewrite the expression

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

Multiply the terms with the same base by adding their exponents

x^{5 + 1} \times 2 (2 x - 4)

Add the numbers

x^{6} \times 2 (2 x - 4)

Use the commutative property to reorder the terms

2 x^{6} (2 x - 4)

Apply the distributive property

2 x^{6} \times 2 x - 2 x^{6} \times 4

Multiply the terms

More Steps

Evaluate

2 x^{6} \times 2 x

Multiply the numbers

4 x^{6} \times x

Multiply the terms

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Evaluate

x^{6} \times x

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

x^{6 + 1}

Add the numbers

x^{7}

4 x^{7}

4 x^{7} - 2 x^{6} \times 4

Solution

4 x^{7} - 8 x^{6}

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Factor the expression

4 x^{6} (x - 2)

Evaluate

x^{5} \times 2 (x \times 1) (2 x - 4)

Remove the parentheses

x^{5} \times 2 x \times 1 \times (2 x - 4)

Any expression multiplied by 1 remains the same

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

Multiply the terms with the same base by adding their exponents

x^{5 + 1} \times 2 (2 x - 4)

Add the numbers

x^{6} \times 2 (2 x - 4)

Use the commutative property to reorder the terms

2 x^{6} (2 x - 4)

Factor the expression

2 x^{6} \times 2 (x - 2)

Solution

4 x^{6} (x - 2)

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Find the roots

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

Evaluate

(x^{5}) \times 2 (x \times 1) (2 x - 4)

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

(x^{5}) \times 2 (x \times 1) (2 x - 4) = 0

Calculate

x^{5} \times 2 (x \times 1) (2 x - 4) = 0

Any expression multiplied by 1 remains the same

x^{5} \times 2 x (2 x - 4) = 0

Multiply

More Steps

Multiply the terms

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

Multiply the terms with the same base by adding their exponents

x^{5 + 1} \times 2 (2 x - 4)

Add the numbers

x^{6} \times 2 (2 x - 4)

Use the commutative property to reorder the terms

2 x^{6} (2 x - 4)

2 x^{6} (2 x - 4) = 0

Elimination the left coefficient

x^{6} (2 x - 4) = 0

Separate the equation into 2 possible cases

x^{6} = 0 2 x - 4 = 0

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

x = 0 2 x - 4 = 0

Solve the equation

More Steps

Evaluate

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