How do you evaluate $a (2 (a^{2} - a) - a (a \frac{a + 1}{a^{2} + a}) - {(- a)}^{2} - \frac{a^{2} - a}{a (a - 1)})$ $a(2(a^2-a)-a(a(a+1)/(a^2+a))-(-a)^2-(a^2-a)/(a(a-1)))$ ?

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Answer 1 · 2017-10-22T16:09:57

$= a (a^{2} - 3 a - 1) = a^{3} - 3 a^{2} - a$ $= a(a^2 -3a - 1) = a^3 -3a^2 -a$

We will simplify term by term and then combine them.

$(2 (a^{2} - a) = 2 a^{2} - 2 a a a a (1)$ $(2(a^2-a) = 2a ^2 - 2a color (white)(aaa) (1)$

$a(a ((a+1) / (a^2+a) ) = a ( a( cancel (a + 1) / (a cancel(a+ 1))))$
$= ( a * cancel a)/ cancel a = a color (white)(aaa) (2)$

$(-a)^2 = a^2 color (white)(aaa) (3)$

$(a^2 - a) / (a (a - 1)) = cancel (a (a - 1)) / cancel (a (a -1) )= 1 color (white)(aaa)$ (4)

Combining all the terms,

$a ( 2a ^2 - 2a - a - a^2 - 1)$

$= a ( a^2 - 3a - 1)$

$= a^3 - 3a^2 - a$

How do you evaluate a(2(a^2-a)-a(a(a+1)/(a^2+a))-(-a)^2-(a^2-a)/(a(a-1)))a(2(a2−a)−a(aa+1a2+a)−(−a)2−a2−aa(a−1))a(2(a^2-a)-a(a(a+1)/(a^2+a))-(-a)^2-(a^2-a)/(a(a-1)))?