Solve 4g^2g-g - ScanMath

Question

Simplify the expression

4 g^{3} - g

Evaluate

4 g^{2} \times g - g

Solution

More Steps

Evaluate

4 g^{2} \times g

Multiply the terms with the same base by adding their exponents

4 g^{2 + 1}

Add the numbers

4 g^{3}

4 g^{3} - g

Show Solution

g (2 g - 1) (2 g + 1)

Evaluate

4 g^{2} \times g - g

Evaluate

More Steps

Evaluate

4 g^{2} \times g

Multiply the terms with the same base by adding their exponents

4 g^{2 + 1}

Add the numbers

4 g^{3}

4 g^{3} - g

Factor out g from the expression

g (4 g^{2} - 1)

Solution

More Steps

Evaluate

4 g^{2} - 1

Rewrite the expression in exponential form

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

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

(2 g - 1) (2 g + 1)

g (2 g - 1) (2 g + 1)

Show Solution

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

Alternative Form

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

Evaluate

4 g^{2} \times g - g

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

4 g^{2} \times g - g = 0

Multiply

More Steps

Multiply the terms

4 g^{2} \times g

Multiply the terms with the same base by adding their exponents

4 g^{2 + 1}

Add the numbers

4 g^{3}

4 g^{3} - g = 0

Factor the expression

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

Separate the equation into 2 possible cases

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

Solve the equation

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Evaluate

4 g^{2} - 1 = 0

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

4 g^{2} = 0 + 1

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

4 g^{2} = 1

Divide both sides

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

Divide the numbers

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

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

g = \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}

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

Separate the equation into 2 possible cases

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

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

Solution

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

Alternative Form

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

Show Solution