Solve (x^2)(x-3)(4x^3)

Question

Simplify the expression

4 x^{6} - 12 x^{5}

Evaluate

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

Multiply the terms with the same base by adding their exponents

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

Add the numbers

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

Use the commutative property to reorder the terms

4 x^{5} (x - 3)

Apply the distributive property

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

Multiply the terms

More Steps

Evaluate

x^{5} \times x

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

x^{5 + 1}

Add the numbers

x^{6}

4 x^{6} - 4 x^{5} \times 3

Solution

4 x^{6} - 12 x^{5}

Show Solution

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

Evaluate

(x^{2}) (x - 3) (4 x^{3})

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

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

Calculate

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

Multiply the terms

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

Multiply

More Steps

Multiply the terms

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

Multiply the terms with the same base by adding their exponents

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

Add the numbers

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

Use the commutative property to reorder the terms

4 x^{5} (x - 3)

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

Elimination the left coefficient

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

Separate the equation into 2 possible cases

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

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

x = 0 x - 3 = 0

Solve the equation

More Steps

Evaluate

x - 3 = 0

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

x = 0 + 3

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

x = 3

x = 0 x = 3

Solution

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

Show Solution