1. find the value of x^2 + 2xy + y^2 if x + y =12
2. (x + 3)^2 - (x + 1)^2
3. simplify (1/b - 1/a) x (b/a - a/b)
4. x^2 + x + 1/4
thankyou
x^2 + 2xy + y^2 = (x + y)(x + y) = (12)(12) = 144
(x + 3)^2 - (x + 1)^2 = [ (x + 3) + (x + 1) ] [ (x + 3) - (x + 1) ] = [2x + 4] [ 2] = 2[x + 2] [2] = 4[x + 2] = 4x + 8
(1/b - 1/a) x (b/a - a/b) = [ 1/a - b/a^2 - a/b^2 + 1/b] [there are other possible forms]
x^2 + x + 1/4 = (x + 1/2)(x + 1/2) = (x + 1/2)^2
x^2 + 2xy + y^2 = (x + y)(x + y) = (12)(12) = 144
(x + 3)^2 - (x + 1)^2 = [ (x + 3) + (x + 1) ] [ (x + 3) - (x + 1) ] = [2x + 4] [ 2] = 2[x + 2] [2] = 4[x + 2] = 4x + 8
(1/b - 1/a) x (b/a - a/b) = [ 1/a - b/a^2 - a/b^2 + 1/b] [there are other possible forms]
x^2 + x + 1/4 = (x + 1/2)(x + 1/2) = (x + 1/2)^2