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

Question

Simplify the expression

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

Evaluate

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

Remove the parentheses

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

Multiply the terms with the same base by adding their exponents

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

Add the numbers

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

Multiply the terms

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

Use the commutative property to reorder the terms

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

Multiply the terms

25 a^{4} (a - 5)

Apply the distributive property

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

Multiply the terms

More Steps

Evaluate

a^{4} \times a

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

a^{4 + 1}

Add the numbers

a^{5}

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

Solution

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

Show Solution

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

Evaluate

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

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

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

Multiply

More Steps

Multiply the terms

a^{2} \times 5 a^{2} \times 5

Multiply the terms with the same base by adding their exponents

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

Add the numbers

a^{4} \times 5 \times 5

Multiply the terms

a^{4} \times 25

Use the commutative property to reorder the terms

25 a^{4}

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

Multiply the terms

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

Elimination the left coefficient

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

Separate the equation into 2 possible cases

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

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

a = 0 a - 5 = 0

Solve the equation

More Steps

Evaluate

a - 5 = 0

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

a = 0 + 5

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

a = 5

a = 0 a = 5

Solution

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

Show Solution