Solve (j-1)(4j-1)

Question

Simplify the expression

4 j^{2} - 5 j + 1

Evaluate

(j - 1) (4 j - 1)

Apply the distributive property

j \times 4 j - j \times 1 - 4 j - (- 1)

Multiply the terms

More Steps

Evaluate

j \times 4 j

Use the commutative property to reorder the terms

4 j \times j

Multiply the terms

4 j^{2}

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

Any expression multiplied by 1 remains the same

4 j^{2} - j - 4 j - (- 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

4 j^{2} - j - 4 j + 1

Solution

More Steps

Evaluate

- j - 4 j

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

(- 1 - 4) j

Subtract the numbers

- 5 j

4 j^{2} - 5 j + 1

Show Solution

Find the roots

j_{1} = \frac{1}{4}, j_{2} = 1

Alternative Form

j_{1} = 0.25, j_{2} = 1

Evaluate

(j - 1) (4 j - 1)

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

(j - 1) (4 j - 1) = 0

Separate the equation into 2 possible cases

j - 1 = 0 4 j - 1 = 0

Solve the equation

More Steps

Evaluate

j - 1 = 0

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

j = 0 + 1

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

j = 1

j = 1 4 j - 1 = 0

Solve the equation

More Steps

Evaluate

4 j - 1 = 0

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

4 j = 0 + 1

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

4 j = 1

Divide both sides

\frac{4 j}{4} = \frac{1}{4}

Divide the numbers

j = \frac{1}{4}

j = 1 j = \frac{1}{4}

Solution

j_{1} = \frac{1}{4}, j_{2} = 1

Alternative Form

j_{1} = 0.25, j_{2} = 1

Show Solution