 welcome again friends so let's now try a few questions on trinomial square expansion so the first question is expand 9x plus 2y plus z whole square so we have learned trinomial square expansion identity so hence a plus b plus c whole square is given as a square plus b square plus c square plus twice a b plus twice b c plus twice c a now all are positive here there is no negative sign so it will be very easy for us to do this so hence it is nothing but 9x whole squared plus 2y whole squared plus z whole squared is it it so you are treating this as a this as b and this as c these are the three terms so you have to deal with three terms separately further it is nothing but 2 times 9x times 2y plus 2 times 2y times z plus 2 times z times 9x okay so hence expanding or simplifying you'll get 9 square is 81 square x square here this is 4 y square plus z square plus 4 9s are 36 x y plus 4 y z plus 18 zx okay so this is what the expansion would look like always take care of this thing that all the you know same power term should be clubbed together okay so it's better to write like this now second one now if you see here there is one catch that there is a minus x and minus 2 y so I will take that whole as a this whole as b and that becomes my c so hence it will be reduced to minus x whole squared plus minus 2 y whole squared plus z square so in this case I don't need to remember the formula different formula for varieties of let's say different signs over there what I mean is you just need to remember only one identity whether it is plus a minus a plus b minus b or plus c minus c accordingly we can change it by replacing plus a by minus a plus b by minus b and plus c by minus c that's it so only one formula will suffice all and then carrying forward here it is nothing but 2 times minus x and minus 2 y plus 2 times minus 2 y times z plus 2 times z times minus x simplifying you'll get x squared plus 4 y squared plus z squared and then it will be wait a minute it was it was there only yes right so hence it is now minus minus becomes plus in the fourth term so it's 4 x y then what minus 4 y z then what minus 2 z x isn't it so x to the power x square minus 4 y square sorry plus 4 y square z square this minus this minus multiplies together becomes plus so it is 4 x y since there was a 2 here hence and this is nothing but minus 4 y z and this is nothing but minus 2 that x this is how you have to expand it dealing with trinomial trinomial squares okay and here is a problem and the problem is a plus b holds a plus b plus c whole squared minus a minus b minus c whole squared we have to simplify so we know this what do we know we know a plus b plus c whole square can be expanded as a square plus b square plus c square plus twice a b plus twice b c plus twice c a so we'll use it directly here so hence the first term will be expanded as a square plus b square plus c square plus twice a b plus twice b c plus twice c a and we have a minus sign so be careful with the sign and then I will be using the square brackets to expand the second term so it will be nothing but a square plus minus b whole square right so I am treating if you see this is nothing but a plus minus b plus minus c whole square so that it becomes easier for me to apply the formula so a square plus minus b square plus minus c squared plus 2 times a times minus b plus 2 times minus b times minus c plus 2 times minus c times a this is the whole expansion so the second step will be a squared full of b square plus c square plus twice a b plus twice b c plus twice c a the first six terms then now let's apply this minus sign to all and open the bracket we'll get minus a squared minus b squared minus c squared why or rather let me do it in one more step so that you guys do not get confused so I will write now this as within brackets a square plus b square plus c square because minus b whole square is b square and minus c whole square is also c square minus twice a b then plus 2 b c and then minus 2 c a I have you understood why these signs so hence minus into minus is plus and rest this is also minus this is also minus so likewise now now expand or open the brackets so you'll get a square plus b square plus c square plus 2 a b plus 2 b c plus 2 c a and then if you open the brackets you'll get minus a square minus b square minus c square plus 2 a b minus 2 b c plus 2 c a and dear friends if you see this is nothing but this a square and a square will go b square b square will go c square c square will go this will go so hence final answer is 4 a b plus 4 c a