Resolving of formula

[LazeFox]

I do understand the 2nd half of the formula, that being 4*k+1, but why is 4*k^2 suddenly in there?

 

[tkhunny]

Have you considered multiplying the binomials (2k+1)(2k+1). What is your result.

Things aren't generally "suddenly in there". There are rules. It's not magic.

What do you get for n? Careful!

 

[Steven G]

Since 2k+1 is odd if k is an integer, then you showed that if you square an odd integer you'll get an odd integer. Do you see that?

 

[Otis]

Here's a pattern for squaring a binomial:

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

Spoiler: Example

(3x - 7)^2 = (3x)^2 + 2(3x)(-7) + (-7)^2

= 9x^2 - 42x + 49

To square a binomial we may (1) square the first term, (2) square the second term, (3) multiply the first and second terms together then double the result and (4) combine the products to get a^2+2ab+b^2.

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[Deleted member 4993]

Have you considered multiplying the binomials (2k+1)(2k+1). What is your result.

Things aren't generally "suddenly in there". There are rules. It's not magic.

What do you get for n? Careful!

Following the advice above:

(2*k + 1)^2 = (2*k + 1) * (2*k + 1)

= 2*k * (2*k + 1) + 1*(2k +1)

= 2*k*2*k + 2*k*1 + 1*2*k + 1*1

= 4k^2 + 2k + 2k + 1

There is your 4k^2 .....