Question 917751: Can anyone explain why 8y(y-2)=0 = (y=0,y=2) I tried the problem solver, but I don't get it. Thanks.
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! if a * b = 0 then either a = 0 or b = 0 or both = 0.
have to be, otherwise the result will not be 0.
take that concept and apply it to 8y * (y-2) = 0
let a = 8y
let b = (y-2)
a * b = 0 becomes 8y * (y-2) = 0
then either 8y = 0 or (y-2) = 0, otherwise the result will not be 0.
solve each for 0.
8y = 0 results in y = 0 when you solve for y.
y-2 = 0 results in y = 2 when you solve for y.
confirm your results by substituting in the original equation.
original equation is 8y * (y-2) = 0
when y = 0, this becomes 0 * -2 = 0 which becomes 0 = 0 which is true.
when y = 2, this becomes 16 * 0 = 0 which becomes 0 = 0 which is true.
the original equation holds true when y = 0 or when y = 2.
that confirms the solution is correct.
solver handled this no problem.
i entered 8y(y-2)=0
i also entered 8y*(y-2)=0
it handled both easily and said the solution was y = 0 or 2.
the explanations it gave under "detailed" may not be the best.
in fact, i had trouble understanding exactly what they were talking about.
if that's what you meant as to why you didn't get it, then i agree.
the reason is as i stated above.
if a * b = 0 then either a has to be equal to 0 or b has to be equal to 0 in order for the result to be equal to 0.
both factors can also be equal to 0 at the same time, but that only occurs in special circumstances when the factors are either the same or mu;ltiples of each other.
example:
(y-2) * (y-2) = 0
both factors are equal to 0 when y = 2.
example again:
(y-2) * (2y-4) = 0
both factors are equal to 0 when y = 2
having both factors equal to 0 at the same time is not essnetial. only one of the factors has to be 0 in order for the result to be equal to 0.
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