Solve - 2t( - 2t^24t-1)

Question

Simplify the expression

16 t^{4} + 2 t

Evaluate

- 2 t (- 2 t^{2} \times 4 t - 1)

Multiply

More Steps

Evaluate

- 2 t^{2} \times 4 t

Multiply the terms

- 8 t^{2} \times t

Multiply the terms with the same base by adding their exponents

- 8 t^{2 + 1}

Add the numbers

- 8 t^{3}

- 2 t (- 8 t^{3} - 1)

Apply the distributive property

- 2 t (- 8 t^{3}) - (- 2 t \times 1)

Multiply the terms

More Steps

Evaluate

- 2 t (- 8 t^{3})

Multiply the numbers

More Steps

Evaluate

- 2 (- 8)

Multiplying or dividing an even number of negative terms equals a positive

2 \times 8

Multiply the numbers

16

16 t \times t^{3}

Multiply the terms

More Steps

Evaluate

t \times t^{3}

Use the product rule a^{n} \times a^{m} = a^{n + m} to simplify the expression

t^{1 + 3}

Add the numbers

t^{4}

16 t^{4}

16 t^{4} - (- 2 t \times 1)

Any expression multiplied by 1 remains the same

16 t^{4} - (- 2 t)

Solution

16 t^{4} + 2 t

Show Solution

Factor the expression

2 t (2 t + 1) (4 t^{2} - 2 t + 1)

Evaluate

- 2 t (- 2 t^{2} \times 4 t - 1)

Multiply

More Steps

Evaluate

- 2 t^{2} \times 4 t

Multiply the terms

- 8 t^{2} \times t

Multiply the terms with the same base by adding their exponents

- 8 t^{2 + 1}

Add the numbers

- 8 t^{3}

- 2 t (- 8 t^{3} - 1)

Factor the expression

More Steps

Evaluate

- 8 t^{3} - 1

Factor out - 1 from the expression

- (8 t^{3} + 1)

Factor the expression

More Steps

Evaluate

8 t^{3} + 1

Calculate

8 t^{3} - 4 t^{2} + 2 t + 4 t^{2} - 2 t + 1

Rewrite the expression

2 t \times 4 t^{2} - 2 t \times 2 t + 2 t + 4 t^{2} - 2 t + 1

Factor out 2 t from the expression

2 t (4 t^{2} - 2 t + 1) + 4 t^{2} - 2 t + 1

Factor out 4 t^{2} - 2 t + 1 from the expression

(2 t + 1) (4 t^{2} - 2 t + 1)

- (2 t + 1) (4 t^{2} - 2 t + 1)

- 2 t (- 1) (2 t + 1) (4 t^{2} - 2 t + 1)

Solution

2 t (2 t + 1) (4 t^{2} - 2 t + 1)

Show Solution

Find the roots

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

Alternative Form

t_{1} = - 0.5, t_{2} = 0

Evaluate

- 2 t (- 2 t^{2} \times 4 t - 1)

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

- 2 t (- 2 t^{2} \times 4 t - 1) = 0

Multiply

More Steps

Multiply the terms

- 2 t^{2} \times 4 t

Multiply the terms

- 8 t^{2} \times t

Multiply the terms with the same base by adding their exponents

- 8 t^{2 + 1}

Add the numbers

- 8 t^{3}

- 2 t (- 8 t^{3} - 1) = 0

Change the sign

2 t (- 8 t^{3} - 1) = 0

Elimination the left coefficient

t (- 8 t^{3} - 1) = 0

Separate the equation into 2 possible cases

t = 0 - 8 t^{3} - 1 = 0

Solve the equation

More Steps

Evaluate

- 8 t^{3} - 1 = 0

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

- 8 t^{3} = 0 + 1

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

- 8 t^{3} = 1

Change the signs on both sides of the equation

8 t^{3} = - 1

Divide both sides

\frac{8 t ^{3}}{8} = \frac{- 1}{8}

Divide the numbers

t^{3} = \frac{- 1}{8}

Use \frac{- a}{b} = \frac{a}{- b} = - \frac{a}{b} to rewrite the fraction

t^{3} = - \frac{1}{8}

Take the 3 -th root on both sides of the equation

3 t^{3} = 3 - \frac{1}{8}

Calculate

t = 3 - \frac{1}{8}

Simplify the root

More Steps

Evaluate

3 - \frac{1}{8}

An odd root of a negative radicand is always a negative

- 3 \frac{1}{8}

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

- \frac{3 1}{3 8}

Simplify the radical expression

- \frac{1}{3 8}

Simplify the radical expression

- \frac{1}{2}

t = - \frac{1}{2}

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

Solution

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

Alternative Form

t_{1} = - 0.5, t_{2} = 0

Show Solution