Solve x^4 -4x^3 4x^2

Question

Simplify the expression

x^{4} - 16 x^{5}

Evaluate

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

Solution

More Steps

Evaluate

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

Multiply the terms

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

Multiply the terms with the same base by adding their exponents

16 x^{3 + 2}

Add the numbers

16 x^{5}

x^{4} - 16 x^{5}

Show Solution

x^{4} (1 - 16 x)

Evaluate

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

Multiply

More Steps

Evaluate

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

Multiply the terms

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

Multiply the terms with the same base by adding their exponents

16 x^{3 + 2}

Add the numbers

16 x^{5}

x^{4} - 16 x^{5}

Rewrite the expression

x^{4} - x^{4} \times 16 x

Solution

x^{4} (1 - 16 x)

Show Solution

x_{1} = 0, x_{2} = \frac{1}{16}

Alternative Form

x_{1} = 0, x_{2} = 0.0625

Evaluate

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

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

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

Multiply

More Steps

Multiply the terms

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

Multiply the terms

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

Multiply the terms with the same base by adding their exponents

16 x^{3 + 2}

Add the numbers

16 x^{5}

x^{4} - 16 x^{5} = 0

Factor the expression

x^{4} (1 - 16 x) = 0

Separate the equation into 2 possible cases

x^{4} = 0 1 - 16 x = 0

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

x = 0 1 - 16 x = 0

Solve the equation

More Steps

Evaluate

1 - 16 x = 0

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

- 16 x = 0 - 1

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

- 16 x = - 1

Change the signs on both sides of the equation

16 x = 1

Divide both sides

\frac{16 x}{16} = \frac{1}{16}

Divide the numbers

x = \frac{1}{16}

x = 0 x = \frac{1}{16}

Solution

x_{1} = 0, x_{2} = \frac{1}{16}

Alternative Form

x_{1} = 0, x_{2} = 0.0625

Show Solution