Solve (8n-1)(n-1)

Question

Simplify the expression

8 n^{2} - 9 n + 1

Evaluate

(8 n - 1) (n - 1)

Apply the distributive property

8 n \times n - 8 n \times 1 - n - (- 1)

Multiply the terms

8 n^{2} - 8 n \times 1 - n - (- 1)

Any expression multiplied by 1 remains the same

8 n^{2} - 8 n - n - (- 1)

If a negative sign or a subtraction symbol appears outside parentheses, remove the parentheses and change the sign of every term within the parentheses

8 n^{2} - 8 n - n + 1

Solution

More Steps

Evaluate

- 8 n - n

Collect like terms by calculating the sum or difference of their coefficients

(- 8 - 1) n

Subtract the numbers

- 9 n

8 n^{2} - 9 n + 1

Show Solution

Find the roots

n_{1} = \frac{1}{8}, n_{2} = 1

Alternative Form

n_{1} = 0.125, n_{2} = 1

Evaluate

(8 n - 1) (n - 1)

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

(8 n - 1) (n - 1) = 0

Separate the equation into 2 possible cases

8 n - 1 = 0 n - 1 = 0

Solve the equation

More Steps

Evaluate

8 n - 1 = 0

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

8 n = 0 + 1

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

8 n = 1

Divide both sides

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

Divide the numbers

n = \frac{1}{8}

n = \frac{1}{8} n - 1 = 0

Solve the equation

More Steps

Evaluate

n - 1 = 0

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

n = 0 + 1

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

n = 1

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

Solution

n_{1} = \frac{1}{8}, n_{2} = 1

Alternative Form

n_{1} = 0.125, n_{2} = 1

Show Solution