Solve (a^3)(a^29)(a-3)

Question

Simplify the expression

9 a^{6} - 27 a^{5}

Evaluate

a^{3} (a^{2} \times 9) (a - 3)

Remove the parentheses

a^{3} \times a^{2} \times 9 (a - 3)

Multiply the terms with the same base by adding their exponents

a^{3 + 2} \times 9 (a - 3)

Add the numbers

a^{5} \times 9 (a - 3)

Use the commutative property to reorder the terms

9 a^{5} (a - 3)

Apply the distributive property

9 a^{5} \times a - 9 a^{5} \times 3

Multiply the terms

More Steps

Evaluate

a^{5} \times a

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

a^{5 + 1}

Add the numbers

a^{6}

9 a^{6} - 9 a^{5} \times 3

Solution

9 a^{6} - 27 a^{5}

Show Solution

a_{1} = 0, a_{2} = 3

Evaluate

(a^{3}) (a^{2} \times 9) (a - 3)

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

(a^{3}) (a^{2} \times 9) (a - 3) = 0

Calculate

a^{3} (a^{2} \times 9) (a - 3) = 0

Use the commutative property to reorder the terms

a^{3} \times 9 a^{2} (a - 3) = 0

Multiply

More Steps

Multiply the terms

a^{3} \times 9 a^{2} (a - 3)

Multiply the terms with the same base by adding their exponents

a^{3 + 2} \times 9 (a - 3)

Add the numbers

a^{5} \times 9 (a - 3)

Use the commutative property to reorder the terms

9 a^{5} (a - 3)

9 a^{5} (a - 3) = 0

Elimination the left coefficient

a^{5} (a - 3) = 0

Separate the equation into 2 possible cases

a^{5} = 0 a - 3 = 0

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

a = 0 a - 3 = 0

Solve the equation

More Steps

Evaluate

a - 3 = 0

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

a = 0 + 3

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

a = 3

a = 0 a = 3

Solution

a_{1} = 0, a_{2} = 3

Show Solution