Solve 3t^28t-3 - ScanMath

Question

Simplify the expression

24 t^{3} - 3

Evaluate

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

Solution

More Steps

Evaluate

3 t^{2} \times 8 t

Multiply the terms

24 t^{2} \times t

Multiply the terms with the same base by adding their exponents

24 t^{2 + 1}

Add the numbers

24 t^{3}

24 t^{3} - 3

Show Solution

Factor the expression

3 (2 t - 1) (4 t^{2} + 2 t + 1)

Evaluate

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

Evaluate

More Steps

Evaluate

3 t^{2} \times 8 t

Multiply the terms

24 t^{2} \times t

Multiply the terms with the same base by adding their exponents

24 t^{2 + 1}

Add the numbers

24 t^{3}

24 t^{3} - 3

Factor out 3 from the expression

3 (8 t^{3} - 1)

Solution

More Steps

Evaluate

8 t^{3} - 1

Rewrite the expression in exponential form

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

Use a^{3} - b^{3} = (a - b) (a^{2} + ab + b^{2}) to factor the expression

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

Evaluate

More Steps

Evaluate

(2 t)^{2}

To raise a product to a power,raise each factor to that power

2^{2} t^{2}

Evaluate the power

4 t^{2}

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

Any expression multiplied by 1 remains the same

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

1 raised to any power equals to 1

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

3 (2 t - 1) (4 t^{2} + 2 t + 1)

Show Solution

Find the roots

t = \frac{1}{2}

Alternative Form

t = 0.5

Evaluate

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

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

3 t^{2} \times 8 t - 3 = 0

Multiply

More Steps

Multiply the terms

3 t^{2} \times 8 t

Multiply the terms

24 t^{2} \times t

Multiply the terms with the same base by adding their exponents

24 t^{2 + 1}

Add the numbers

24 t^{3}

24 t^{3} - 3 = 0

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

24 t^{3} = 0 + 3

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

24 t^{3} = 3

Divide both sides

\frac{24 t ^{3}}{24} = \frac{3}{24}

Divide the numbers

t^{3} = \frac{3}{24}

Cancel out the common factor 3

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}

Solution

More Steps

Evaluate

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

More Steps

Evaluate

38

Write the number in exponential form with the base of 2

3 2^{3}

Reduce the index of the radical and exponent with 3

2

\frac{1}{2}

t = \frac{1}{2}

Alternative Form

t = 0.5

Show Solution