Show that a^3 + b^3 = (a + b)(a^2

Science & Mathematics by Anonymous 2018-06-09 14:03:11

Social Science

Show that a^3 + b^3 = (a + b)(a^2 – ab + b^2) ?

4 answers

Anonymous

RHS= (a+b)(a^2-ab+b^2)= a^3-ba^2+ab^2+ba^2 -ab^2+b^3= a^3+b^3= LHS
Anonymous

[ a + b ] [ a^2 - ab + b^2 ] a^3 - a^2b + ab^2 ____a^2b - ab^2 + b^3 a^4 + b^3
Anonymous

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

a³ + b³ = a³ - a²b + ab² + a²b - ab² + b³ (2nd and 4th terms cancel, as do the 3rd and 5th) = a(a² - ab + b²) + b(a² - ab + b²) = (a + b)(a² - ab + b²)