Solve (x-5)(x^2 5x^25)

Question

Simplify the expression

25 x^{5} - 125 x^{4}

Evaluate

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

Remove the parentheses

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

Multiply the terms with the same base by adding their exponents

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

Add the numbers

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

Multiply the terms

(x - 5) x^{4} \times 25

Use the commutative property to reorder the terms

(x - 5) \times 25 x^{4}

Multiply the terms

25 x^{4} (x - 5)

Apply the distributive property

25 x^{4} \times x - 25 x^{4} \times 5

Multiply the terms

More Steps

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}

25 x^{5} - 25 x^{4} \times 5

Solution

25 x^{5} - 125 x^{4}

Show Solution

x_{1} = 0, x_{2} = 5

Evaluate

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

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

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

Multiply

More Steps

Multiply the terms

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

Multiply the terms with the same base by adding their exponents

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

Add the numbers

x^{4} \times 5 \times 5

Multiply the terms

x^{4} \times 25

Use the commutative property to reorder the terms

25 x^{4}

(x - 5) \times 25 x^{4} = 0

Multiply the terms

25 x^{4} (x - 5) = 0

Elimination the left coefficient

x^{4} (x - 5) = 0

Separate the equation into 2 possible cases

x^{4} = 0 x - 5 = 0

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

x = 0 x - 5 = 0

Solve the equation

More Steps

Evaluate

x - 5 = 0

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

x = 0 + 5

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

x = 5

x = 0 x = 5

Solution

x_{1} = 0, x_{2} = 5

Show Solution