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

Question

Simplify the expression

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

Evaluate

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

Remove the parentheses

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

Multiply the terms with the same base by adding their exponents

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

Add the numbers

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

Use the commutative property to reorder the terms

4 x^{5} (3 - x)

Apply the distributive property

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

Multiply the numbers

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

Solution

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}

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

Show Solution

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

Evaluate

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

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

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

Multiply

More Steps

Multiply the terms

x^{2} \times 4 x^{3}

Multiply the terms with the same base by adding their exponents

x^{2 + 3} \times 4

Add the numbers

x^{5} \times 4

Use the commutative property to reorder the terms

4 x^{5}

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

Elimination the left coefficient

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

Separate the equation into 2 possible cases

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

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

x = 0 3 - x = 0

Solve the equation

More Steps

Evaluate

3 - x = 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

Change the signs on both sides of the equation

x = 3

x = 0 x = 3

Solution

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

Show Solution