If you're seeing this message, it means we're having trouble loading external resources on our website.

If you're behind a web filter, please make sure that the domains *.kastatic.org and *.kasandbox.org are unblocked.

Main content
Current time:0:00Total duration:2:25

Factoring using the perfect square pattern


Video transcript

we need to factor 25 X to the fourth minus 30x squared plus 9 and this looks really daunting because we have something to the fourth power here and then the middle term is to the second power but there's something about this that might pop out at you the thing that pops out at me at least is that 25 is a perfect square X to the 4th is a perfect square so 25 X to the fourth is a perfect square and 9 is also a perfect square so maybe this is the square of some binomial and to confirm it this center term has to be 2 times the product of the terms that you're squaring on either end let me explain that a little bit better so 25 X to the fourth that is the same thing as 5 x squared squared right so it's a perfect square 9 is the exact same thing as well it could be plus or minus 3 squared it could be either one now what is 30x squared well what happens if we take five times plus or minus three so remember this needs to be two times the product of what's inside the square the square root of this and the square root of that so if we take given that there's a negative sign here and five is positive we want to take the negative three right that's the only we're going to get a negative over there so let's just try it with negative three so what is what is two times two times five x squared 5x squared times negative 3 times negative 3 what is this well 2 times 5x squared is 10x squared times negative 3 it is equal to negative 30x squared it is equal to negative 30x squared we know that this is a perfect square so we can just rewrite this as this is equal to this is equal to 5 x squared let me do it the same color 5 x squared minus 3 minus 3 times 5 x squared minus 3 times 5 x squared minus 3 and we saw in the last video why this works and if you want to verify it for yourself multiply this out you will get 25 X to the fourth minus 30x squared plus 9