Mathematics

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Expansion problems using suitable formulaeFollowing formulae are got by multiplying out the brackets.e.g., (a + b)2 = (a + b)(a + b)= a(a + b) + b(a + b)= a2 + ab + ba + b2= a2 + 2ab + b2(1) (a + b)2 = a2 + 2ab + b2(2) (a - b)2 = a2 - 2ab + b2(3) (a + b) (a - b) = a2 - b2(4) (i) (x + a) (x + b) = x2 + (a + b)x + ab(ii) (x + a) (x - b) = x2 + (a - b)x - ab(iii) (x - a) (x - b) = x2 + (- a - b)x + ab
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21= 100 - 42 = 58Example 5 :Expand: (a + 3b - 4c)2Suggested Answer :(a + 3b - 4c)2 = (a)2 + (3b)2 + (-4c)2 + 2[(a) (3b) + (3b) (-4c)+ (-4c) (a)]= a2 + 9b2 + 16c2 + 6ab - 24bc - 8acMore Expansion problems with algebraic identities

2011-10-24 20:01:02 補充：
Example 6 :

If x2 + y2 + z2 = 38, x + y + z = 10, find xy + yz + zx.

2011-10-24 20:01:32 補充：
Suggested Answer :

We have (x2 + y2 + z2) + 2 (xy + yz + zx) = (x + y + z)2

38 + 2 (xy + yz + zx) = (10)2

2011-10-24 20:02:25 補充：
= 62