What is (x+y-1)^2-(x-y+1)^2 ?

The solution to (x+y-1)^2-(x-y+1)^2 is 4xy-4x

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simplify (x+y-1)^2-(x-y+1)^2

simplify

(x + y - 1)^{2} - (x - y + 1)^{2}

4 x y - 4 x

Solution steps

(x + y - 1)^{2} - (x - y + 1)^{2}

Expand

(x + y - 1)^{2} : x^{2} + 2 x y - 2 x + y^{2} - 2 y + 1

= x^{2} + 2 x y - 2 x + y^{2} - 2 y + 1 - (x - y + 1)^{2}

Expand

- (x - y + 1)^{2} : - x^{2} + 2 x y - 2 x - y^{2} + 2 y - 1

= x^{2} + 2 x y - 2 x + y^{2} - 2 y + 1 - x^{2} + 2 x y - 2 x - y^{2} + 2 y - 1

Group like terms

= x^{2} - x^{2} + 2 x y + 2 x y - 2 x - 2 x + y^{2} - y^{2} - 2 y + 2 y + 1 - 1

Add similar elements:

x^{2} - x^{2} = 0

= 2 x y + 2 x y - 2 x - 2 x + y^{2} - y^{2} - 2 y + 2 y + 1 - 1

Add similar elements:

2 x y + 2 x y = 4 x y

= 4 x y - 2 x - 2 x + y^{2} - y^{2} - 2 y + 2 y + 1 - 1

Add similar elements:

- 2 x - 2 x = - 4 x

= 4 x y - 4 x + y^{2} - y^{2} - 2 y + 2 y + 1 - 1

Add similar elements:

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

= 4 x y - 4 x - 2 y + 2 y + 1 - 1

Add similar elements:

- 2 y + 2 y = 0

= 4 x y - 4 x + 1 - 1

Subtract the numbers:

1 - 1 = 0

= 4 x y - 4 x

p (x) + 5 (x)

f (x) + 6

x^{2} - 11 x + 302 x^{2} - 36

(7 m^{3} n)^{- 2}

\frac{( w ^{\frac{5}{7}} )}{( \frac{3}{4} )}