Solve t-4t^2 2t^3

Question

Simplify the expression

t - 8 t^{5}

Evaluate

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

Solution

More Steps

Evaluate

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

Multiply the terms

8 t^{2} \times t^{3}

Multiply the terms with the same base by adding their exponents

8 t^{2 + 3}

Add the numbers

8 t^{5}

t - 8 t^{5}

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Factor the expression

t (1 - 8 t^{4})

Evaluate

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

Multiply

More Steps

Evaluate

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

Multiply the terms

8 t^{2} \times t^{3}

Multiply the terms with the same base by adding their exponents

8 t^{2 + 3}

Add the numbers

8 t^{5}

t - 8 t^{5}

Rewrite the expression

t - t \times 8 t^{4}

Solution

t (1 - 8 t^{4})

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Find the roots

t_{1} = - \frac{4 2}{2}, t_{2} = 0, t_{3} = \frac{4 2}{2}

Alternative Form

t_{1} \approx - 0.594604, t_{2} = 0, t_{3} \approx 0.594604

Evaluate

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

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

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

Multiply

More Steps

Multiply the terms

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

Multiply the terms

8 t^{2} \times t^{3}

Multiply the terms with the same base by adding their exponents

8 t^{2 + 3}

Add the numbers

8 t^{5}

t - 8 t^{5} = 0

Factor the expression

t (1 - 8 t^{4}) = 0

Separate the equation into 2 possible cases

t = 0 1 - 8 t^{4} = 0

Solve the equation

More Steps

Evaluate

1 - 8 t^{4} = 0

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

- 8 t^{4} = 0 - 1

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

- 8 t^{4} = - 1

Change the signs on both sides of the equation

8 t^{4} = 1

Divide both sides

\frac{8 t ^{4}}{8} = \frac{1}{8}

Divide the numbers

t^{4} = \frac{1}{8}

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

t = \pm 4 \frac{1}{8}

Simplify the expression

More Steps

Evaluate

4 \frac{1}{8}

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

\frac{4 1}{4 8}

Simplify the radical expression

\frac{1}{4 8}

Multiply by the Conjugate

\frac{4 8 ^{3}}{4 8 \times 4 8 ^{3}}

Simplify

\frac{2 ^{2} 4 2}{4 8 \times 4 8 ^{3}}

Multiply the numbers

\frac{2 ^{2} 4 2}{2 ^{3}}

Reduce the fraction

\frac{4 2}{2}

t = \pm \frac{4 2}{2}

Separate the equation into 2 possible cases

t = \frac{4 2}{2} t = - \frac{4 2}{2}

t = 0 t = \frac{4 2}{2} t = - \frac{4 2}{2}

Solution

t_{1} = - \frac{4 2}{2}, t_{2} = 0, t_{3} = \frac{4 2}{2}

Alternative Form

t_{1} \approx - 0.594604, t_{2} = 0, t_{3} \approx 0.594604

Show Solution