Question

simplify (x-2y+3)^2+(x+2y-3)^2​

Answer 1

By using (a+b+c)² formula

we can simplify it

Answer 2

Answer:

Let us expand the given expression:

(x – 2y + 3)2 + (x + 2y – 3)2 = [(x)2 +(-2y)2 + (3)2 +{2 ×(x)×(- 2y)} +{2 ×(- 2y)× (3)} + {2 ×(x)×(3)}] + [(x)2 + (2y)2 + (-3)2 + {2×(x)×(2y)} +{2×(2y)×(- 3)} +{2 ×(x)×(-3)}]

By using the formula,

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

= [x2 + 4y2 + 9 + {– 4xy} + {– 12y} + {6x}] + [x2 + 4y2 + 9 + {4xy} + {– 12y} + {– 6x}]

= [x2 + 4y2 + 9 – 4xy – 12y + 6x] + [x2 + 4y2 + 9 + 4xy – 12y – 6x]

= x2 + 4y2 + 9 – 4xy – 12y + 6x + x2 + 4y2 + 9 + 4xy – 12y – 6x

= 2x2 + 8y2 + 18 – 24y

∴ (x – 2y + 3)2 + (x + 2y – 3)2 = 2x2 + 8y2 + 18 – 24y