Solve (a-3)(a^24a^2)

Question

Simplify the expression

4 a^{5} - 12 a^{4}

Evaluate

(a - 3) (a^{2} \times 4 a^{2})

Remove the parentheses

(a - 3) a^{2} \times 4 a^{2}

Multiply the terms with the same base by adding their exponents

(a - 3) a^{2 + 2} \times 4

Add the numbers

(a - 3) a^{4} \times 4

Use the commutative property to reorder the terms

(a - 3) \times 4 a^{4}

Multiply the terms

4 a^{4} (a - 3)

Apply the distributive property

4 a^{4} \times a - 4 a^{4} \times 3

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}

4 a^{5} - 4 a^{4} \times 3

Solution

4 a^{5} - 12 a^{4}

Show Solution

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

Evaluate

(a - 3) (a^{2} \times 4 a^{2})

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

(a - 3) (a^{2} \times 4 a^{2}) = 0

Multiply

More Steps

Multiply the terms

a^{2} \times 4 a^{2}

Multiply the terms with the same base by adding their exponents

a^{2 + 2} \times 4

Add the numbers

a^{4} \times 4

Use the commutative property to reorder the terms

4 a^{4}

(a - 3) \times 4 a^{4} = 0

Multiply the terms

4 a^{4} (a - 3) = 0

Elimination the left coefficient

a^{4} (a - 3) = 0

Separate the equation into 2 possible cases

a^{4} = 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