Q: Factor ab minus 2ac plus b squared minus 2bc?

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ab-2ac+b^2-2bc

If you mean (a-b+c)^2, then... a^2 - ab + ac - ab + b^2 - bc + ac - bc + c^2 = a^2 + b^2 + c^2 - 2ab + 2ac - 2bc.

It's easy to evalute (a + b + c)2..... Let x = (a + b)....then expand (x + c)2 as you would normally in the case of binomial expansion......which is : (x + c)2 = x2 + c2 + 2xc ......(1) Now, replace x with (a + b) in (1).....then it becomes....... (a + b)2 + c2 + 2.(a + b).c .....(2) Just a little more to be done here ( now we expand (2) in the last step)........ a2 + b2 + 2ab + c2 + 2ac + 2bc (rearranging this we get) a2 + b2 + c2 + 2ab + 2bc + 2ac . this happens to be the expansion for (a + b = c)2

2ab+2bc+2ac=Surface area of a rectangular prism C=2 B=10 A=5 2(5)(10)+2(10)(2)+2(5)(2)= 100+40+20=160cm^2

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4

ab-2ac+b^2-2bc

(a + b)(b - 2c)

(a + b)(b - 2c)

This is known as the Cosine Rule.

(2a + c)(4a2 - 2ac + c2)

(a+b+c)²=a²+b²+c²+ 2ab+2bc+2ac

3ac + 2ca = 3ac + 2ac = (3 + 2)(ac) = 5ac

If you mean (a-b+c)^2, then... a^2 - ab + ac - ab + b^2 - bc + ac - bc + c^2 = a^2 + b^2 + c^2 - 2ab + 2ac - 2bc.

(a+b-c)2 = a2 + b2 +c2 +2ab - 2bc - 2ac

a2+2ab+b2+2ac+2bc+c2+2ad+2ae+2bd+2be+2cd+2ce+d2+2de+e2

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