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

Question

Simplify the expression

96 x^{4} - 96 x^{3} - 18 x^{5}

Evaluate

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

Multiply the terms

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

Multiply the terms

More Steps

Evaluate

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

Apply the distributive property

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

Multiply the numbers

24 x^{3} - 6 x^{3} \times 3 x

Multiply the terms

More Steps

Evaluate

6 x^{3} \times 3 x

Multiply the numbers

18 x^{3} \times x

Multiply the terms

18 x^{4}

24 x^{3} - 18 x^{4}

(24 x^{3} - 18 x^{4}) (x - 4)

Apply the distributive property

24 x^{3} \times x - 24 x^{3} \times 4 - 18 x^{4} \times x - (- 18 x^{4} \times 4)

Multiply the terms

More Steps

Evaluate

x^{3} \times x

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

x^{3 + 1}

Add the numbers

x^{4}

24 x^{4} - 24 x^{3} \times 4 - 18 x^{4} \times x - (- 18 x^{4} \times 4)

Multiply the numbers

24 x^{4} - 96 x^{3} - 18 x^{4} \times x - (- 18 x^{4} \times 4)

Multiply the terms

More Steps

Evaluate

x^{4} \times x

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

x^{4 + 1}

Add the numbers

x^{5}

24 x^{4} - 96 x^{3} - 18 x^{5} - (- 18 x^{4} \times 4)

Multiply the numbers

24 x^{4} - 96 x^{3} - 18 x^{5} - (- 72 x^{4})

If a negative sign or a subtraction symbol appears outside parentheses, remove the parentheses and change the sign of every term within the parentheses

24 x^{4} - 96 x^{3} - 18 x^{5} + 72 x^{4}

Solution

More Steps

Evaluate

24 x^{4} + 72 x^{4}

Collect like terms by calculating the sum or difference of their coefficients

(24 + 72) x^{4}

Add the numbers

96 x^{4}

96 x^{4} - 96 x^{3} - 18 x^{5}

Show Solution

Find the roots

x_{1} = 0, x_{2} = \frac{4}{3}, x_{3} = 4

Alternative Form

x_{1} = 0, x_{2} = 1. \dot{3}, x_{3} = 4

Evaluate

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

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

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

Multiply the terms

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

Multiply the terms

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

Elimination the left coefficient

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

Separate the equation into 3 possible cases

x^{3} = 0 4 - 3 x = 0 x - 4 = 0

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

x = 0 4 - 3 x = 0 x - 4 = 0

Solve the equation

More Steps

Evaluate

4 - 3 x = 0

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

- 3 x = 0 - 4

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

- 3 x = - 4

Change the signs on both sides of the equation

3 x = 4

Divide both sides

\frac{3 x}{3} = \frac{4}{3}

Divide the numbers

x = \frac{4}{3}

x = 0 x = \frac{4}{3} x - 4 = 0

Solve the equation

More Steps

Evaluate

x - 4 = 0

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

x = 0 + 4

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

x = 4

x = 0 x = \frac{4}{3} x = 4

Solution

x_{1} = 0, x_{2} = \frac{4}{3}, x_{3} = 4

Alternative Form

x_{1} = 0, x_{2} = 1. \dot{3}, x_{3} = 4

Show Solution