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to the power of question

HI Zeyu or any fellow school mate, I know this super basic but how can we effective translate to the power of something into (X+1)(x-1) for example. Here is the real question:

Sequence question No. 32 on the notes, (n+5)2 - (n+1)2 = (n+5+n+1)(n+5-n-1)

the “2” above is to the power of 2… how can I make to the power of into n+5+n+1???

another example would be 7x11n -7x11n-1 would become
7x11n-1(11-1)

the above “n” and “n-1” is to the power of…

please enlighten me!

a^2 - b^2 = (a+b)(a-b)
a^3 - b^3 =(a-b)(a^2+ab+b^2)
a^3+b^3 = (a+b)(a^2 - ab +b^2)
(a+b)^2 = a^2 +2ab +b^2

these are basic formulas you have to memorize.

For calculation of exponents, please read your OG.

Exponents and Square roots.pdf (493.5 KB)