Exponents and Polynomials Help;

[gijas]

(3m^3 - 2m^2 + 1)^2

I get this:

(3m^3)^2 (2m^2)^2 (1)^2

= 9m^5 - 4m^4 + 1

Is this correct? If not please explain so I know how to solve this type of problem correctly. Thanks.

 

[soroban]

Hello, gijas!

\(\displaystyle (3m^3 - 2m^2 + 1)^2\)

\(\displaystyle \text{I get this: }\3m^3)^2 - (2m^2)^2 + (1)^2 \;=\; 9m^5 - 4m^4 + 1\)

\(\displaystyle \text{Is this correct?}\) . No!

\(\displaystyle (3m^3 - 2m^2 + 1)^2 \;=\;(3m^3 - 2m^2 + 1)(3m^3 - 2m^2 + 1)\)

Now do the multiplication . . . carefully.

 

[gijas]

Hello, gijas!


\(\displaystyle (3m^3 - 2m^2 + 1)^2 \;=\;(3m^3 - 2m^2 + 1)(3m^3 - 2m^2 + 1)\)

Now do the multiplication . . . carefully.

9m^6 - 12m^5 + 4m^4 + 6m^3 -4m^2 + 1 ???

 

[lookagain]

Correct.
You can check if correct by substituting a value for m; keep it simple, try m=1

If substituting a value for m in the original and in the expanded one gives
the same value, then the check is inconclusive, as there may be errors
in the terms for that particular m value that cancel out, etc.

However, if the values for a specific m are correctly substituted and evaluated,
but the results don't match, then you can state with certainty that the
original expression is not equal to the expanded expression.