Solve (x^2 2x^3)(x^2-2x^3)

Question

Simplify the expression

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

Evaluate

(x^{2} \times 2 x^{3}) (x^{2} - 2 x^{3})

Remove the parentheses

x^{2} \times 2 x^{3} (x^{2} - 2 x^{3})

Multiply the terms with the same base by adding their exponents

x^{2 + 3} \times 2 (x^{2} - 2 x^{3})

Add the numbers

x^{5} \times 2 (x^{2} - 2 x^{3})

Use the commutative property to reorder the terms

2 x^{5} (x^{2} - 2 x^{3})

Apply the distributive property

2 x^{5} \times x^{2} - 2 x^{5} \times 2 x^{3}

Multiply the terms

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Evaluate

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

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

x^{5 + 2}

Add the numbers

x^{7}

2 x^{7} - 2 x^{5} \times 2 x^{3}

Solution

More Steps

Evaluate

2 x^{5} \times 2 x^{3}

Multiply the numbers

4 x^{5} \times x^{3}

Multiply the terms

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Evaluate

x^{5} \times x^{3}

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

x^{5 + 3}

Add the numbers

x^{8}

4 x^{8}

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

Show Solution

Factor the expression

2 x^{7} (1 - 2 x)

Evaluate

(x^{2} \times 2 x^{3}) (x^{2} - 2 x^{3})

Remove the parentheses

x^{2} \times 2 x^{3} (x^{2} - 2 x^{3})

Multiply

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Evaluate

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

Multiply the terms with the same base by adding their exponents

x^{2 + 3} \times 2

Add the numbers

x^{5} \times 2

Use the commutative property to reorder the terms

2 x^{5}

2 x^{5} (x^{2} - 2 x^{3})

Factor the expression

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Evaluate

x^{2} - 2 x^{3}

Rewrite the expression

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

Factor out x^{2} from the expression

x^{2} (1 - 2 x)

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

Solution

2 x^{7} (1 - 2 x)

Show Solution

Find the roots

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

Alternative Form

x_{1} = 0, x_{2} = 0.5

Evaluate

(x^{2} \times 2 x^{3}) (x^{2} - 2 x^{3})

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

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

Multiply

More Steps

Multiply the terms

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

Multiply the terms with the same base by adding their exponents

x^{2 + 3} \times 2

Add the numbers

x^{5} \times 2

Use the commutative property to reorder the terms

2 x^{5}

2 x^{5} (x^{2} - 2 x^{3}) = 0

Elimination the left coefficient

x^{5} (x^{2} - 2 x^{3}) = 0

Separate the equation into 2 possible cases

x^{5} = 0 x^{2} - 2 x^{3} = 0

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

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

Solve the equation

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Evaluate

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

Factor the expression

x^{2} (1 - 2 x) = 0

Separate the equation into 2 possible cases

x^{2} = 0 1 - 2 x = 0

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

x = 0 1 - 2 x = 0

Solve the equation

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Evaluate

1 - 2 x = 0

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

- 2 x = 0 - 1

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

- 2 x = - 1

Change the signs on both sides of the equation

2 x = 1

Divide both sides

\frac{2 x}{2} = \frac{1}{2}

Divide the numbers

x = \frac{1}{2}

x = 0 x = \frac{1}{2}

x = 0 x = 0 x = \frac{1}{2}

Find the union

x = 0 x = \frac{1}{2}

Solution

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

Alternative Form

x_{1} = 0, x_{2} = 0.5

Show Solution