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June 11th, 2013, 02:38 AM   #1
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Formulae Required

What is the formula for (a+b+c+d)^2 . Please help
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June 11th, 2013, 02:47 AM   #2
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(a + b + c + d) ? a + b + c + d + 2ab + 2ac + 2ad + 2bc + 2bd + 2cd
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June 11th, 2013, 02:48 AM   #3
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Re: Formulae Required

Quote:
Originally Posted by qamath09
What is the formula for (a+b+c+d)^2 . Please help
Well, you're going to get

a^2 + b^2 + c^2 + d^2

... that's easy... then every multiplicative combination of 2 letters twice...

from left to right you will get

ab + ac + ad + bc + bd + cd

twice, so finally,

a^2 + b^2 + c^2 + d^2 + 2(ab + ac + ad + bc + bd + cd)

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June 11th, 2013, 03:45 AM   #4
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Re: Formulae Required


(image not to scale)
The surface of the square is the product of the length of the sides. (a + b + c + d) * (a + b + c + d) = (a + b + c + d)^2.
The surface of the square is also the sum of the surfaces of all the smaller rectangles.
Which is a+ab+ac+ad+ba+b+...+cd+d.
Simplifying gives a + b + c + d + 2ab + 2ac + 2ad + 2bc + 2bd + 2cd.

So (a + b + c + d)^2 = a + b + c + d + 2ab + 2ac + 2ad + 2bc + 2bd + 2cd.

Note: every square is also a rectangle so even if for example a = c, then ac can still be called rectangle.
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June 11th, 2013, 06:18 AM   #5
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Re: Formulae Required

Or, by the distributive property:

etc.

-Dan
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June 11th, 2013, 07:12 AM   #6
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Re: Formulae Required

(a+b+c+d)^2 =(a+b)^2 +(c+d)^2 +2(a+b)(c+d)
=a^2 +b^2 +c^2 +d^2 +2(ab+bc+cd+da+ac+bd).
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June 11th, 2013, 10:18 PM   #7
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Re: Formulae Required

(a+b+c+d)
=> ( (a+b) + (c+d) )
=> (a+b) + (c+d) + 2(a+b)(c+d)
=> a + b + 2ab + c + d + 2cd + 2 (ac + bc + ad + bd)
=> a + b + c + d + 2ab + 2cd + 2ac + 2bc + 2ad + 2bd

(a+b) = a + b + 2ab
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