Solve 360t 10t^3 - 120t^2

Question

Simplify the expression

3600 t^{4} - 120 t^{2}

Evaluate

360 t \times 10 t^{3} - 120 t^{2}

Solution

More Steps

Evaluate

360 t \times 10 t^{3}

Multiply the terms

3600 t \times t^{3}

Multiply the terms with the same base by adding their exponents

3600 t^{1 + 3}

Add the numbers

3600 t^{4}

3600 t^{4} - 120 t^{2}

Show Solution

Factor the expression

120 t^{2} (30 t^{2} - 1)

Evaluate

360 t \times 10 t^{3} - 120 t^{2}

Multiply

More Steps

Evaluate

360 t \times 10 t^{3}

Multiply the terms

3600 t \times t^{3}

Multiply the terms with the same base by adding their exponents

3600 t^{1 + 3}

Add the numbers

3600 t^{4}

3600 t^{4} - 120 t^{2}

Rewrite the expression

120 t^{2} \times 30 t^{2} - 120 t^{2}

Solution

120 t^{2} (30 t^{2} - 1)

Show Solution

Find the roots

t_{1} = - \frac{30}{30}, t_{2} = 0, t_{3} = \frac{30}{30}

Alternative Form

t_{1} \approx - 0.182574, t_{2} = 0, t_{3} \approx 0.182574

Evaluate

360 t \times 10 t^{3} - 120 t^{2}

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

360 t \times 10 t^{3} - 120 t^{2} = 0

Multiply

More Steps

Multiply the terms

360 t \times 10 t^{3}

Multiply the terms

3600 t \times t^{3}

Multiply the terms with the same base by adding their exponents

3600 t^{1 + 3}

Add the numbers

3600 t^{4}

3600 t^{4} - 120 t^{2} = 0

Factor the expression

120 t^{2} (30 t^{2} - 1) = 0

Divide both sides

t^{2} (30 t^{2} - 1) = 0

Separate the equation into 2 possible cases

t^{2} = 0 30 t^{2} - 1 = 0

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

t = 0 30 t^{2} - 1 = 0

Solve the equation

More Steps

Evaluate

30 t^{2} - 1 = 0

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

30 t^{2} = 0 + 1

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

30 t^{2} = 1

Divide both sides

\frac{30 t ^{2}}{30} = \frac{1}{30}

Divide the numbers

t^{2} = \frac{1}{30}

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

t = \pm \frac{1}{30}

Simplify the expression

More Steps

Evaluate

\frac{1}{30}

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

\frac{1}{30}

Simplify the radical expression

\frac{1}{30}

Multiply by the Conjugate

\frac{30}{30 \times 30}

When a square root of an expression is multiplied by itself,the result is that expression

\frac{30}{30}

t = \pm \frac{30}{30}

Separate the equation into 2 possible cases

t = \frac{30}{30} t = - \frac{30}{30}

t = 0 t = \frac{30}{30} t = - \frac{30}{30}

Solution

t_{1} = - \frac{30}{30}, t_{2} = 0, t_{3} = \frac{30}{30}

Alternative Form

t_{1} \approx - 0.182574, t_{2} = 0, t_{3} \approx 0.182574

Show Solution