Question

Square the following general examples to determine the general rule for squaring a binomial:

Answer 1

Answer:

See explanation below.

Step-by-step explanation:

For part a we have the following expression:

$(a+b)^2 = a^2 +2ab + b^2$

And for part b we got:

$(a-b)^2 = a^2 -2ab +b^2$

On general we have the following formula:

$(a+b)^n =\sum_{k=0}^n (nCk) a^{n-k} b^k$

We see that if n=2 we have this:

$(a+b)^2 =\sum_{k=0}^2 (2Ck) a^{2-k} b^k$

$(a+b)^2 = (2C0) a^2 b^0 + (2C1)a^{2-1} b^1 + (2C2) a^{2-2} b^2$

$(a+b)^2 = a^2 +2ab + b^2$

And for the other possibility we have:

$(a+b)^n =\sum_{k=0}^n (-1)^k (nCk) a^{n-k} b^k$

We see that if n=2 we have this:

$(a+b)^2 =\sum_{k=0}^2 (2Ck) a^{2-k} b^k$

$(a+b)^2 = (-1)^0 (2C0) a^2 b^0 +(-1)^1 (2C1)a^{2-1} b^1 + (-1)^2 (2C2) a^{2-2} b^2$

$(a+b)^2 = a^2 +2ab + b^2$

So then we have the general expression for any binomial term elevated at any power.