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

The solution to (x+2)^2-(y-1)^2 is x^2+4x-y^2+2y+3

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

simplify

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

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

Solution steps

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

Expand

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

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

Expand

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

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

Group like terms

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

Subtract the numbers:

4 - 1 = 3

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

(- 14 + \frac{3}{2} b) - (1 + \frac{8}{2} b)

\frac{2 \cdot ( 2 - \frac{3}{2} ) ^{2}}{2 ^{2} \cdot 3 ^{6}}

\frac{11}{44}

- 3 x \cdot x

(5 x y - 3) - (2 - 4 x y)