Solve 4x*x^3-x^2 - ScanMath

Question

Simplify the expression

4 x^{4} - x^{2}

Evaluate

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

Solution

More Steps

Evaluate

4 x \times x^{3}

Multiply the terms with the same base by adding their exponents

4 x^{1 + 3}

Add the numbers

4 x^{4}

4 x^{4} - x^{2}

Show Solution

Factor the expression

x^{2} (2 x - 1) (2 x + 1)

Evaluate

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

Evaluate

More Steps

Evaluate

4 x \times x^{3}

Multiply the terms with the same base by adding their exponents

4 x^{1 + 3}

Add the numbers

4 x^{4}

4 x^{4} - x^{2}

Factor out x^{2} from the expression

x^{2} (4 x^{2} - 1)

Solution

More Steps

Evaluate

4 x^{2} - 1

Rewrite the expression in exponential form

(2 x)^{2} - 1^{2}

Use a^{2} - b^{2} = (a - b) (a + b) to factor the expression

(2 x - 1) (2 x + 1)

x^{2} (2 x - 1) (2 x + 1)

Show Solution

Find the roots

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

Alternative Form

x_{1} = - 0.5, x_{2} = 0, x_{3} = 0.5

Evaluate

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

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

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

Multiply

More Steps

Multiply the terms

4 x \times x^{3}

Multiply the terms with the same base by adding their exponents

4 x^{1 + 3}

Add the numbers

4 x^{4}

4 x^{4} - x^{2} = 0

Factor the expression

x^{2} (4 x^{2} - 1) = 0

Separate the equation into 2 possible cases

x^{2} = 0 4 x^{2} - 1 = 0

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

x = 0 4 x^{2} - 1 = 0

Solve the equation

More Steps

Evaluate

4 x^{2} - 1 = 0

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

4 x^{2} = 0 + 1

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

4 x^{2} = 1

Divide both sides

\frac{4 x ^{2}}{4} = \frac{1}{4}

Divide the numbers

x^{2} = \frac{1}{4}

Take the root of both sides of the equation and remember to use both positive and negative roots

x = \pm \frac{1}{4}

Simplify the expression

More Steps

Evaluate

\frac{1}{4}

To take a root of a fraction,take the root of the numerator and denominator separately

\frac{1}{4}

Simplify the radical expression

\frac{1}{4}

Simplify the radical expression

\frac{1}{2}

x = \pm \frac{1}{2}

Separate the equation into 2 possible cases

x = \frac{1}{2} x = - \frac{1}{2}

x = 0 x = \frac{1}{2} x = - \frac{1}{2}

Solution

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

Alternative Form

x_{1} = - 0.5, x_{2} = 0, x_{3} = 0.5

Show Solution