Solve 2k^(2) 2k-4

Question

Simplify the expression

4 k^{3} - 4

Evaluate

2 k^{2} \times 2 k - 4

Solution

More Steps

Evaluate

2 k^{2} \times 2 k

Multiply the terms

4 k^{2} \times k

Multiply the terms with the same base by adding their exponents

4 k^{2 + 1}

Add the numbers

4 k^{3}

4 k^{3} - 4

Show Solution

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

Evaluate

2 k^{2} \times 2 k - 4

Evaluate

More Steps

Evaluate

2 k^{2} \times 2 k

Multiply the terms

4 k^{2} \times k

Multiply the terms with the same base by adding their exponents

4 k^{2 + 1}

Add the numbers

4 k^{3}

4 k^{3} - 4

Factor out 4 from the expression

4 (k^{3} - 1)

Solution

More Steps

Evaluate

k^{3} - 1

Rewrite the expression in exponential form

k^{3} - 1^{3}

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

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

Any expression multiplied by 1 remains the same

(k - 1) (k^{2} + k + 1^{2})

1 raised to any power equals to 1

(k - 1) (k^{2} + k + 1)

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

Show Solution

k = 1

Evaluate

2 k^{2} \times 2 k - 4

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

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

Multiply

More Steps

Multiply the terms

2 k^{2} \times 2 k

Multiply the terms

4 k^{2} \times k

Multiply the terms with the same base by adding their exponents

4 k^{2 + 1}

Add the numbers

4 k^{3}

4 k^{3} - 4 = 0

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

4 k^{3} = 0 + 4

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

4 k^{3} = 4

Divide both sides

\frac{4 k ^{3}}{4} = \frac{4}{4}

Divide the numbers

k^{3} = \frac{4}{4}

Divide the numbers

More Steps

Evaluate

\frac{4}{4}

Reduce the numbers

\frac{1}{1}

Calculate

1

k^{3} = 1

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

3 k^{3} = 31

Calculate

k = 31

Solution

k = 1

Show Solution