Answer:
See explanation below.
Step-by-step explanation:
For part a we have the following expression:
[tex] (a+b)^2 = a^2 +2ab + b^2[/tex]
And for part b we got:
[tex] (a-b)^2 = a^2 -2ab +b^2[/tex]
On general we have the following formula:
[tex] (a+b)^n =\sum_{k=0}^n (nCk) a^{n-k} b^k[/tex]
We see that if n=2 we have this:
[tex] (a+b)^2 =\sum_{k=0}^2 (2Ck) a^{2-k} b^k[/tex]
[tex] (a+b)^2 = (2C0) a^2 b^0 + (2C1)a^{2-1} b^1 + (2C2) a^{2-2} b^2[/tex]
[tex] (a+b)^2 = a^2 +2ab + b^2[/tex]
And for the other possibility we have:
[tex] (a+b)^n =\sum_{k=0}^n (-1)^k (nCk) a^{n-k} b^k[/tex]
We see that if n=2 we have this:
[tex] (a+b)^2 =\sum_{k=0}^2 (2Ck) a^{2-k} b^k[/tex]
[tex] (a+b)^2 = (-1)^0 (2C0) a^2 b^0 +(-1)^1 (2C1)a^{2-1} b^1 + (-1)^2 (2C2) a^{2-2} b^2[/tex]
[tex] (a+b)^2 = a^2 +2ab + b^2[/tex]
So then we have the general expression for any binomial term elevated at any power.
