solve (y-1)(y-2)=0

Question

solve the equation (y-1)(y-2)=0

Answer 1

Recall the Zero-Product Property, which states that if the product of two factors is zero then at least one of the factors must be zero. That is, if  a·b=0  then  a=0  and/or  b=0.

Given:     (y - 1)(y - 2) = 0

The equation you are given states that the product of the two factors (y - 1) and (y - 2) is equal to 0. With this, and by the zero-product property, then the factor (y - 1) must be equal o zero and/or the factor (y - 2) must be equal to zero. That is,

          y - 1 = 0          and/or           y - 2 = 0

Solving for y in both cases, we arrive at the following:

     y - 1 = 0                       ;                   y - 2 = 0

      + 1    + 1                                           + 2   + 2

 _______________                             ________________

  y - 1 + 1 = 0 + 1                               y - 2 + 2 = 0 + 2

            y = 1                                                y = 2

Thus, the solutions for the equation  (y - 1)(y - 2) = 0  are  1  and  2

Answer 2

This problem is set up very nicely for you.

First I'm just going to point out a property of numbers.  When you multiply two numbers, the only way the product can be 0 is if at least one of the numbers is 0.  In other words if x * y = 0 then either x or y must also be 0.  (both x and y could also be zero).

This means that in your equation either (y - 1) or (y - 2) must equal zero.  Let's try each case.

y - 1 = 0

y = 1 (add 1 to both sides)

or

y - 2 = 0

y = 2 (add 2 to both sides)

This means that y can either equal 1 or 2, a good way to represent this answer is like this:

y = 1, 2

In order to drive the point home, lets plug in both values for y to make sure it works:

lets say that y = 1 first.

(1 - 1) * (1 - 2) = 0

(0) * (-1) = 0

0 * (-1) = 0

0 = 0

So we know y = 1 is a valid answer.  Now lets try y = 2

(2 - 1) * (2 - 2) = 0

(1) * (0) = 0

1 * 0 = 0

0 = 0

We have just confirmed that both answers y = 1 and y = 2 will satisfy the equation (y-1)(y-2) = 0.

Hope that helps.