Solve (5x^6)(x-2) (x-2) 2 (3x^5)

Question

Simplify the expression

30 x^{13} - 120 x^{12} + 120 x^{11}

Evaluate

5 x^{6} (x - 2) (x - 2) \times 2 \times 3 x^{5}

Multiply the terms

More Steps

Evaluate

5 \times 2 \times 3

Multiply the terms

10 \times 3

Multiply the numbers

30

30 x^{6} (x - 2) (x - 2) x^{5}

Multiply the terms with the same base by adding their exponents

30 x^{6 + 5} (x - 2) (x - 2)

Add the numbers

30 x^{11} (x - 2) (x - 2)

Multiply the terms

30 x^{11} (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

30 x^{11} (x^{2} - 4 x + 4)

Apply the distributive property

30 x^{11} \times x^{2} - 30 x^{11} \times 4 x + 30 x^{11} \times 4

Multiply the terms

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Evaluate

x^{11} \times x^{2}

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

x^{11 + 2}

Add the numbers

x^{13}

30 x^{13} - 30 x^{11} \times 4 x + 30 x^{11} \times 4

Multiply the terms

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Evaluate

30 x^{11} \times 4 x

Multiply the numbers

120 x^{11} \times x

Multiply the terms

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Evaluate

x^{11} \times x

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

x^{11 + 1}

Add the numbers

x^{12}

120 x^{12}

30 x^{13} - 120 x^{12} + 30 x^{11} \times 4

Solution

30 x^{13} - 120 x^{12} + 120 x^{11}

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Find the roots

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

Evaluate

(5 x^{6}) (x - 2) (x - 2) \times 2 (3 x^{5})

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

(5 x^{6}) (x - 2) (x - 2) \times 2 (3 x^{5}) = 0

Multiply the terms

5 x^{6} (x - 2) (x - 2) \times 2 (3 x^{5}) = 0

Multiply the terms

5 x^{6} (x - 2) (x - 2) \times 2 \times 3 x^{5} = 0

Multiply the terms

More Steps

Multiply the terms

5 x^{6} (x - 2) (x - 2) \times 2 \times 3 x^{5}

Multiply the terms

More Steps

Evaluate

5 \times 2 \times 3

Multiply the terms

10 \times 3

Multiply the numbers

30

30 x^{6} (x - 2) (x - 2) x^{5}

Multiply the terms with the same base by adding their exponents

30 x^{6 + 5} (x - 2) (x - 2)

Add the numbers

30 x^{11} (x - 2) (x - 2)

Multiply the terms

30 x^{11} (x - 2)^{2}

30 x^{11} (x - 2)^{2} = 0

Elimination the left coefficient

x^{11} (x - 2)^{2} = 0

Separate the equation into 2 possible cases

x^{11} = 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

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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