SOLUTION: Evaluate A = (a^2 − 3a +1)^2 − (1− a)(−2a +1)(1− 3a) . Then WITHOUT doing any further calculation write down the value of B = (a^2 + 3a +1)^2 −

Question 823760: Evaluate A = (a^2 − 3a +1)^2 − (1− a)(−2a +1)(1− 3a) . Then WITHOUT doing any
further calculation write down the value of B = (a^2 + 3a +1)^2 − (1+ a)(2a +1)(1+ 3a) .
Found 2 solutions by richwmiller, KMST:
Answer by richwmiller(17219) (Show Source): You can put this solution on YOUR website!
a^4 for both A and B
Answer by KMST(5328) (Show Source): You can put this solution on YOUR website!
Without doing any calculation we can see that
and are both polynomial functions of with degree 4.
Without doing much calculation we can see that

and .
So, the fact that makes calculations easier.
We do not even need to calculate to see that
.
We can calculate the value of the functions for
, , , .

In sum

We know that the polynomial of degree 4 has

and since 5 points uniquely determine a degree 4 polynomial,
just like 2 points uniquely determine a line,

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SOLUTION: Evaluate A = (a^2 &#8722; 3a +1)^2 &#8722; (1&#8722; a)(&#8722;2a +1)(1&#8722; 3a) . Then WITHOUT doing any further calculation write down the value of B = (a^2 + 3a +1)^2 &#8722;

SOLUTION: Evaluate A = (a^2 − 3a +1)^2 − (1− a)(−2a +1)(1− 3a) . Then WITHOUT doing any further calculation write down the value of B = (a^2 + 3a +1)^2 −