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# Factoring difference of squares: leading coefficient ≠ 1

## Video transcript

let's see if we can factor the expression 45 x squared minus 125 so whenever I see something like this I have a second-degree term here I must have a subtraction sign my tension my temptation just to look at this as a difference of squares we've already seen this multiple times we've already seen that if we have something of the form if we have something of the form a squared minus B squared that this can be factored as a plus B times a minus B so let's look over here well over here it's not obvious that this right over here is a perfect square neither is it obvious that this right over here is a perfect square so it's not clear to me that this is a difference of squares but what is interesting is that both 45 and 125 have have some factors in common and the one that jumps out at me is 5 so let's see if we can factor out a 5 and by doing that whether we can get something that's a little bit closer to this pattern right over here so if we factor out a 5 this becomes 5 times 5 times well 45 x squared divided by 5 is going to be 9 x squared and then 125 divided by 5 is 25 is 25 now this is interesting 9 x squared that's a perfect square if we call this if we call this a squared then that tells us that a would be equal to 3 X 3 X the whole thing squared is 9x squared similarly I can never say similarly correctly 25 is clearly just 5 squared so in this case if we're looking at if we're looking at this template B would be equal to 5 so now this is a difference of squares and we can factor it completely so we can't forget our 5 up front that we factored out so it's going to be 5 times a plus B so let me write this so it's going to be 5 times a plus B times 5 times a minus B so it's 5 times a plus B times a minus B so let me write the B's down plus B and minus B and we're done five times 3x plus 5 times 3x minus 5 is 45 x squared minus 1 25 factored out