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

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

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

simplify

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

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

Solution steps

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

Join

- 2 - \frac{1}{( x + y ) ^{2}} : \frac{- 2 x ^{2} - 4 x y - 2 y ^{2} - 1}{( x + y ) ^{2}}

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

Cross-cancel common factor:

(x + y)^{2}

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

\frac{( x ^{k} )}{( k + 4 ) 4 ^{k}}

\frac{( sec ( θ ) ) ( 1 + tan ( θ ) )}{sec ( θ ) + csc ( θ )}

\frac{y - 8}{( y ^{2} - 4 ) ( y + 3 ) ( y ^{2} + 4 y - 12 )}

\frac{( x - 20 ) ( x - 45 ) ( x - 55 )}{3750}

\frac{d}{d q} ((c) (0.0003 q^{2} - 0.03 q + 4))

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