Question 1168999

Factor,

a^2 - 14a + 49 - b^2

I know you can use difference of squares but i have no idea how to do it
<pre>You need to 1st group the expression as follows since you want to have a perfect square INTEGER/VARIABLE to the UTMOST right-side of the expression: {{{(a^2 - 14a + 49) - b^2}}}
Now, we use the "ac" method for the first grouped expression, which involves finding 2 INTEGERS that when MULTIPLIED gives us "+ 49", and when added, gives us "- 14."
These FACTORS are simply - 7 and - 7. We then get: {{{(a - 7)(a - 7) - b^2}}}, and finally: {{{highlight_green(matrix(1,4, (a - 7)^2 - b^2, ",", or, (a - 7 - b)(a - 7 + b)))}}}