Question

Multiply a² + a - 3 by 2a² - a +5​

Answer 1

Answer:

We are trying to find a3−2a2−2a2−1a3 given that a−1a=2 .

Some quick manipulation before we start that will help:

First, a−1a=2

Next,

(a−1a)2

=a2−2(a)(1a)+1a2

=a2+1a2−2

Another way of expressing the expression squared is (a−1a)2=22=4

So a2+1a2=6 . Remember this.

And:

(a−1a)3

=a3−3(a2)(1a)+3(a)(1a2)−1a3

=a3−3a+3a−1a3

=a3−3(a−1a)−1a3

=a3−1a3−6

Similarly , we can also say that (a−1a)3=23=8 .

So (a−1a)3=14

With that, our solution becomes easier.

a3−2a2−2a2−1a3

=(a3−1a3)−2(a2+1a2)

=14−2(6)

=2

your answer is 2