Solve 4(n^(2) 2n 1)-1

Question

Simplify the expression

8 n^{3} - 1

Evaluate

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

Remove the parentheses

4 n^{2} \times 2 n \times 1 - 1

Solution

More Steps

Evaluate

4 n^{2} \times 2 n \times 1

Rewrite the expression

4 n^{2} \times 2 n

Multiply the terms

8 n^{2} \times n

Multiply the terms with the same base by adding their exponents

8 n^{2 + 1}

Add the numbers

8 n^{3}

8 n^{3} - 1

Show Solution

Factor the expression

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

Evaluate

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

Evaluate

More Steps

Evaluate

4 (n^{2} \times 2 n \times 1)

Remove the parentheses

4 n^{2} \times 2 n \times 1

Rewrite the expression

4 n^{2} \times 2 n

Multiply the terms

8 n^{2} \times n

Multiply the terms with the same base by adding their exponents

8 n^{2 + 1}

Add the numbers

8 n^{3}

8 n^{3} - 1

Rewrite the expression in exponential form

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

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

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

Evaluate

More Steps

Evaluate

(2 n)^{2}

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

2^{2} n^{2}

Evaluate the power

4 n^{2}

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

Any expression multiplied by 1 remains the same

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

Solution

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

Show Solution

Find the roots

n = \frac{1}{2}

Alternative Form

n = 0.5

Evaluate

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

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

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

Multiply the terms

More Steps

Multiply the terms

n^{2} \times 2 n \times 1

Rewrite the expression

n^{2} \times 2 n

Multiply the terms with the same base by adding their exponents

n^{2 + 1} \times 2

Add the numbers

n^{3} \times 2

Use the commutative property to reorder the terms

2 n^{3}

4 \times 2 n^{3} - 1 = 0

Multiply the numbers

8 n^{3} - 1 = 0

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

8 n^{3} = 0 + 1

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

8 n^{3} = 1

Divide both sides

\frac{8 n ^{3}}{8} = \frac{1}{8}

Divide the numbers

n^{3} = \frac{1}{8}

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

3 n^{3} = 3 \frac{1}{8}

Calculate

n = 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}

n = \frac{1}{2}

Alternative Form

n = 0.5

Show Solution