SOLUTION: I know the chosen topic has nothing to do with this but I couldn’t find the topic for this problem. Use polynomial identities and number properties to perform the calculation.

Algebra ->  Sequences-and-series -> SOLUTION: I know the chosen topic has nothing to do with this but I couldn’t find the topic for this problem. Use polynomial identities and number properties to perform the calculation.      Log On


   

Question 1200167: I know the chosen topic has nothing to do with this but I couldn’t find the topic for this problem.
Use polynomial identities and number properties to perform the calculation.
109^2
Found 4 solutions by josgarithmetic, math_tutor2020, ikleyn, MathTherapy:
Answer by josgarithmetic(39618) About Me  (Show Source):
You can put this solution on YOUR website!
?
??

Maybe something this way:
%281%2A10%5E2%2B9%2A10%5E0%29%281%2A10%5E2%2B9%2A10%5E0%29, and just perform the multiplication as if you would for binomials.

10 takes the place of a variable such as x.

%2810%5E2%2B9%29%2810%5E2%2B9%29
%2810%5E2%29%5E2%2B9%2A10%5E2%2B9%2A10%5E2%2B9%2A9
10%5E4%2B18%2A10%5E2%2B9%5E2
10000%2B1800%2B81
11881

Answer by math_tutor2020(3817) About Me  (Show Source):
You can put this solution on YOUR website!

Treat 109 as 100+9

The task of computing 109^2 is the same as (100+9)^2

Then use the identity
(a+b)^2 = a^2 + 2ab + b^2
where
a = 100
b = 9
I'll let the student perform the computation.

A similar example:
27^2 = (20+7)^2
27^2 = 20^2 + 2*20*7 + 7^2
27^2 = 400 + 280 + 49
27^2 = 680 + 49
27^2 = 729
You can use a calculator to confirm.

Answer by ikleyn(52788) About Me  (Show Source):
You can put this solution on YOUR website!
.
I know the chosen topic has nothing to do with this but I couldn’t find the topic for this problem.
Use polynomial identities and number properties to perform the calculation highlight%28mentally_without_using_a_calculator%29.
109^2
~~~~~~~~~~~~~~~~~~~ 

Use  109%5E2 = %28110-1%29%5E2 = 110%5E2 - 2%2A110 + 1 = 12100 - 220 + 1 = 11880 + 1 = 11900 - 20 + 1 = 11880 + 1 = 11881.    ANSWER

This way.


================


May I ask you please do not include in your future posts this very first line about the topic.

It does not carry any useful info,  and we,  the tutors at this forum,  never look at the  " topic ".

It's a pity to spend time reading unnecessary information.


Simply say  " could you help me please " - it is just enough.   Necessary and enough.


Also necessary to post your "thanks" after receiving a tutor's response.


It is much more important than posting many words that mean nothing.



Answer by MathTherapy(10552) About Me  (Show Source):
You can put this solution on YOUR website!
I know the chosen topic has nothing to do with this but I couldn’t find the topic for this problem.

Use polynomial identities and number properties to perform the calculation.

109^2