Solve 5x^(4)(x^5)^(4)(x-1)^(3)(x 8)^(2)

Question

Simplify the expression

320 x^{29} - 960 x^{28} + 960 x^{27} - 320 x^{26}

Evaluate

5 x^{4} (x^{5})^{4} (x - 1)^{3} (x \times 8)^{2}

Multiply the exponents

5 x^{4} \times x^{5 \times 4} (x - 1)^{3} (x \times 8)^{2}

Use the commutative property to reorder the terms

5 x^{4} \times x^{5 \times 4} (x - 1)^{3} (8 x)^{2}

Multiply the numbers

5 x^{4} \times x^{20} (x - 1)^{3} (8 x)^{2}

Multiply the terms with the same base by adding their exponents

5 x^{4 + 20} (x - 1)^{3} (8 x)^{2}

Add the numbers

5 x^{24} (x - 1)^{3} (8 x)^{2}

Simplify

320 x^{24} (x - 1)^{3} x^{2}

Multiply the terms

More Steps

Evaluate

x^{24} \times x^{2}

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

x^{24 + 2}

Add the numbers

x^{26}

320 x^{26} (x - 1)^{3}

Expand the expression

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Evaluate

(x - 1)^{3}

Use (a - b)^{3} = a^{3} - 3 a^{2} b + 3 a b^{2} - b^{3} to expand the expression

x^{3} - 3 x^{2} \times 1 + 3 x \times 1^{2} - 1^{3}

Calculate

x^{3} - 3 x^{2} + 3 x - 1

320 x^{26} (x^{3} - 3 x^{2} + 3 x - 1)

Apply the distributive property

320 x^{26} \times x^{3} - 320 x^{26} \times 3 x^{2} + 320 x^{26} \times 3 x - 320 x^{26} \times 1

Multiply the terms

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Evaluate

x^{26} \times x^{3}

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

x^{26 + 3}

Add the numbers

x^{29}

320 x^{29} - 320 x^{26} \times 3 x^{2} + 320 x^{26} \times 3 x - 320 x^{26} \times 1

Multiply the terms

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Evaluate

320 x^{26} \times 3 x^{2}

Multiply the numbers

960 x^{26} \times x^{2}

Multiply the terms

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Evaluate

x^{26} \times x^{2}

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

x^{26 + 2}

Add the numbers

x^{28}

960 x^{28}

320 x^{29} - 960 x^{28} + 320 x^{26} \times 3 x - 320 x^{26} \times 1

Multiply the terms

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Evaluate

320 x^{26} \times 3 x

Multiply the numbers

960 x^{26} \times x

Multiply the terms

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Evaluate

x^{26} \times x

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

x^{26 + 1}

Add the numbers

x^{27}

960 x^{27}

320 x^{29} - 960 x^{28} + 960 x^{27} - 320 x^{26} \times 1

Solution

320 x^{29} - 960 x^{28} + 960 x^{27} - 320 x^{26}

Show Solution

Find the roots

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

Evaluate

5 x^{4} (x^{5})^{4} (x - 1)^{3} (x \times 8)^{2}

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

5 x^{4} (x^{5})^{4} (x - 1)^{3} (x \times 8)^{2} = 0

Use the commutative property to reorder the terms

5 x^{4} (x^{5})^{4} (x - 1)^{3} (8 x)^{2} = 0

Evaluate the power

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Evaluate

(x^{5})^{4}

Transform the expression

x^{5 \times 4}

Multiply the numbers

x^{20}

5 x^{4} \times x^{20} (x - 1)^{3} (8 x)^{2} = 0

Multiply

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Multiply the terms

5 x^{4} \times x^{20} (x - 1)^{3} (8 x)^{2}

Multiply the terms with the same base by adding their exponents

5 x^{4 + 20} (x - 1)^{3} (8 x)^{2}

Add the numbers

5 x^{24} (x - 1)^{3} (8 x)^{2}

Simplify

320 x^{24} (x - 1)^{3} x^{2}

320 x^{24} (x - 1)^{3} x^{2} = 0

Elimination the left coefficient

x^{24} (x - 1)^{3} x^{2} = 0

Separate the equation into 3 possible cases

x^{24} = 0 (x - 1)^{3} = 0 x^{2} = 0

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

x = 0 (x - 1)^{3} = 0 x^{2} = 0

Solve the equation

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Evaluate

(x - 1)^{3} = 0

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

x - 1 = 0

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

x = 0 + 1

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

x = 1

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

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

x = 0 x = 1 x = 0

Find the union

x = 0 x = 1

Solution

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

Show Solution