Solve (1-5z)(2-5z)

Question

(1 - 5 z) (2 - 5 z)

Simplify the expression

2 - 15 z + 25 z^{2}

Evaluate

(1 - 5 z) (2 - 5 z)

Apply the distributive property

1 \times 2 - 1 \times 5 z - 5 z \times 2 - (- 5 z \times 5 z)

Any expression multiplied by 1 remains the same

2 - 1 \times 5 z - 5 z \times 2 - (- 5 z \times 5 z)

Any expression multiplied by 1 remains the same

2 - 5 z - 5 z \times 2 - (- 5 z \times 5 z)

Multiply the numbers

2 - 5 z - 10 z - (- 5 z \times 5 z)

Multiply the terms

More Steps

Evaluate

- 5 z \times 5 z

Multiply the numbers

- 25 z \times z

Multiply the terms

- 25 z^{2}

2 - 5 z - 10 z - (- 25 z^{2})

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

2 - 5 z - 10 z + 25 z^{2}

Solution

More Steps

Evaluate

- 5 z - 10 z

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

(- 5 - 10) z

Subtract the numbers

- 15 z

2 - 15 z + 25 z^{2}

Show Solution

Find the roots

z_{1} = \frac{1}{5}, z_{2} = \frac{2}{5}

Alternative Form

z_{1} = 0.2, z_{2} = 0.4

Evaluate

(1 - 5 z) (2 - 5 z)

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

(1 - 5 z) (2 - 5 z) = 0

Separate the equation into 2 possible cases

1 - 5 z = 0 2 - 5 z = 0

Solve the equation

More Steps

Evaluate

1 - 5 z = 0

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

- 5 z = 0 - 1

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

- 5 z = - 1

Change the signs on both sides of the equation

5 z = 1

Divide both sides

\frac{5 z}{5} = \frac{1}{5}

Divide the numbers

z = \frac{1}{5}

z = \frac{1}{5} 2 - 5 z = 0

Solve the equation

More Steps

Evaluate

2 - 5 z = 0

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

- 5 z = 0 - 2

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

- 5 z = - 2

Change the signs on both sides of the equation

5 z = 2

Divide both sides

\frac{5 z}{5} = \frac{2}{5}

Divide the numbers

z = \frac{2}{5}

z = \frac{1}{5} z = \frac{2}{5}

Solution

z_{1} = \frac{1}{5}, z_{2} = \frac{2}{5}

Alternative Form

z_{1} = 0.2, z_{2} = 0.4

Show Solution