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How to expand the trinomial?

How to expand the trinomial?

Let we will learn to expand the square of a trinomial (a + b + c). Let (b + c) = x       Then (a + b + c)2 = (a + x)2 = a2+ 2ax + x2

                         = a2 + 2a (b + c) + (b + c)2

                         = a2 + 2ab + 2ac + (b2 + c2 + 2bc) 

                         = a2 + b2 + c2 + 2ab + 2bc + 2ca

Therefore, (a + b + c)2 = a2 + b2+ c2 + 2ab + 2bc + 2ca
Here are some examples only for u......
I)
2l – 3m + 4n)2

Solution: 

(2l – 3m + 4n)2

We know, (a - b + c)2 = a2 + b2 + c2 – 2ab - 2bc + 2ca

Here a = 2l, b = -3m and c = 4n

(2l + (-3m) + 4n)2

= (2l)2 + (3m)2 + (4n)2 + 2 (2l) (-3m) + 2 (-3m) (4n) + 2 (4n) (2l) 

= 4l2 + 9m2 + 16n2 – 12lm – 24mn + 16nl

Therefore, (2l – 3m + 4n)2 = 4l2+ 9m2 + 16n2 – 12lm – 24mn + 16nl


(iii) (3x – 2y – z)2

Solution: 

(3x – 2y – z)