uh, i dont understand this quadratic question (1 Viewer)

[wolf7]

how does this equation work

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

is there some technique getting there or is it just is

 

[Mystic Crusader]

quadratic

a^2 + b^2 =(a+b)^2 -2ab
RHS = (a+b)^2 -2ab
= a^2 + 2ab +b^2 -2ab by expanding the brackets
=a^2+ b^2 collecting like terms
=LHS

i hope this helps you =)

 

[wolf7]

thanx people, i understand how to use it

 

[icycloud]

Just a note: this can be expanded for a⁴ + b⁴, a⁶ + b⁶, aⁿ + bⁿ where n is an even number.

As such:

a⁴ + b⁴
= (a²)² + (b²)²
= (a² + b²)² - (√2 ab)²
= (a² + b² - √2 ab)(a² + b² + √2 ab)

This sort of manipulation might come in handy, if not in 2U then in 3U or 4U.