Question 203415
Difference of two squares: {{{a^2 - b^2 = (a + b)(a - b)}}}
{{{b^2 = 18}}}
First let's get a difference by subtracting 18 from both sides:
{{{b^2 - 18 = 0}}}
Now we need to write this as a difference of squares. b^2 is already a square. Next we need to write 18 as a square. What squared is 18? Answer: {{{sqrt(18)}}}. Now we have:
{{{b^2 - (sqrt(18))^2 = 0}}}
which is a difference of squares. We can rewrite this as:
{{{(b + sqrt(18))(b - sqrt(18)) = 0}}}
In order for this (or any) product to be zero, one of the factors must be zero (Zero Product Property). So
{{{b + sqrt(18) = 0}}} or {{{b - sqrt(18) = 0}}}
Solving these we get:
{{{b = -sqrt(18)}}} or {{{b = sqrt(18)}}}
We can simplify these square roots.
{{{sqrt(18) = sqrt(9*2) = sqrt(9)*sqrt(2) = 3sqrt(2)}}}
So the simplified answers:
{{{b = -3sqrt(2)}}} or {{{b = 3sqrt(2)}}}<br>
Using the same steps on {{{z^2 = 13}}} we get {{{z = sqrt(13)}}} or {{{z = -sqrt(13)}}}