00:00Here in the question we have to find the length of PQR in AP.
00:02And we have been asked the value of this equation.
00:04So first of all we will call it the standard formula of AP.
00:08But we should not consider it as A plus D, A plus 2D, A plus 3D
00:12Why would A minus D, A and A plus D agree?
00:16So that it becomes easier to do the calculation
00:19Then later you put the value
00:21Cube of A minus D, plus 3A minus D, into A plus D, into A minus D, plus A plus
00:29whole cube of D plus A plus D
00:32Now we get the formula for the whole cube of A minus D.
00:35If there was no formula, we would simply multiply the whole square of A minus D by A minus D
00:41do
00:41So the cube of A minus D will change in our foot.
00:44But if we know the formula then we will write the formula.
00:46A cube minus D cube minus 3A square D plus 3AD square
00:52plus 3, what does this become identity, A minus B into A plus B
00:56What is this identity, A square minus B square
01:00So this becomes A square minus D square into A minus D
01:05Oh, it's gone from minus D to plus D today. Let's say A becomes A, 2A.
01:09whole cube of plus A plus D, A cube plus D cube plus 3A square D plus 3D square
01:16Now A cube added to A cube is 2A cube, minus D cube to plus D cube
01:22cancel, minus 3A square D to plus 3A square D cancel, plus 3AD square, this is D
01:30square A and square AD is the same thing, just like 2 into 3 can be written as 3 into 2,
01:36This becomes 6AD square, solve by putting this term in this way.
01:43You will do it, next, multiply 2 by 3 to get 6, that is, both these terms together
01:496A is now multiplied by 6A in the bracket, 6A into A square, 6A cube, minus 6A
01:57D square, 6A cube minus 6A, D square, 6A cube plus 2A cube, how much is it, 8A cube, plus this
02:06In, this minus
02:07In, both of them cancel out in the event, so then in the matter 8A cube, this is what we have value in the equation
02:13If you had put, what was the value of A, equal to Q, that is, now in place of A, you have Q
02:18We will put, because in the format of option Q, we will put Q in place of 8A, so it becomes,
02:248Q
02:24Q, which means our answer will be option number D.
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