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# simple way to calculate binomials if you know opposite sign answer? watch

1. so if you know the answer to (2+3x)^4 or the expansion of it how would you calculate the expansion of (2-3x)^4 from this
2. (Original post by jonjoshelvey21)
so if you know the answer to (2+3x)^4 or the expansion of it how would you calculate the expansion of (2-3x)^4 from this
Take the original expansion and replace with , since . You'll notice that even powers remain unaffected but the odd powers switch signs.
3. (Original post by RDKGames)
Take the original expansion and replace with , since . You'll notice that even powers remain unaffected but the odd powers switch signs.
4. (Original post by RDKGames)
Take the original expansion and replace with , since . You'll notice that even powers remain unaffected but the odd powers switch signs.
what if the question were the other way round like if you knew the answer to (2-3x)^4 but wanted to know (2+3x)^4??
5. (Original post by jonjoshelvey21)
what if the question were the other way round like if you knew the answer to (2-3x)^4 but wanted to know (2+3x)^4??
It’s obvious isnt it? Every odd power will be negative so just make them positive. Every occurance of x you see, factor into (-x) then replace this by (x)
6. (Original post by RDKGames)
It’s obvious isnt it? Every odd power will be negative so just make them positive. Every occurance of x you see, factor into (-x) then replace this by (x)
what so wherever an x is present you plug in -x?
7. (Original post by jonjoshelvey21)
what so wherever an x is present you plug in -x?
No. Whereever x is, say you have , you want to factor it in such a way that you have -x, so then replace every -x with x, to get
8. (Original post by RDKGames)
No. Whereever x is, say you have , you want to factor it in such a way that you have -x, so then replace every -x with x, to get
thanks sorry to be confusing but for my very first question would you factor it in such a way to get -x as well ????
9. (2+3x)^4 = 81x^4 + 216^3 + 216x^2 + 96x + 16
1 x 3x^4 x 2^0 = 81x^4
4 x 3x^3 x 2^1 = 216x^3
6 x 3x^2 x 2^2 = 216x^2
4 x 3x^1 x 2^3 = 96x
1 x 3x^0 x 2^4 = 16

It's basically going to be the same answer however it will alternate between positive and negative coefficients, for example (-2^1) = -1 but (-2^2) = 4 and (-2^3) = -8

(2-3x)^4
1 x (-3x^4) x 2^0 = 81x^4
4 x (-3x^3) x 2^1 = -216x^3
6 x (-3x^2) x 2^2 = 216x^2
4 x (-3x^1) x 2^3 = -96x
1 x (-3x^0) x 2^4 = 16

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