What is (x+y)^2-(2x-y)^2 ?

The solution to (x+y)^2-(2x-y)^2 is -3x^2+6xy

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simplify (x+y)^2-(2x-y)^2

simplify

(x + y)^{2} - (2 x - y)^{2}

- 3 x^{2} + 6 x y

Solution steps

(x + y)^{2} - (2 x - y)^{2}

Expand

(x + y)^{2} : x^{2} + 2 x y + y^{2}

= x^{2} + 2 x y + y^{2} - (2 x - y)^{2}

Expand

- (2 x - y)^{2} : - 4 x^{2} + 4 x y - y^{2}

= x^{2} + 2 x y + y^{2} - 4 x^{2} + 4 x y - y^{2}

Group like terms

= x^{2} - 4 x^{2} + 2 x y + 4 x y + y^{2} - y^{2}

Add similar elements:

x^{2} - 4 x^{2} = - 3 x^{2}

= - 3 x^{2} + 2 x y + 4 x y + y^{2} - y^{2}

Add similar elements:

2 x y + 4 x y = 6 x y

= - 3 x^{2} + 6 x y + y^{2} - y^{2}

Add similar elements:

y^{2} - y^{2} = 0

= - 3 x^{2} + 6 x y

2 a x - 4 b x + 2 a y - 4 b y

- 58

(5 - 2 i) + (3 + 3 i)

(a - b) (a^{2} - ab + b^{2})

(0.8) (6.16)