The answer is: [A]: (x + 2) (x² − 2x + 4). _______________________________ Explanation: _____________________________ Note the formula: ___________________ a³ + b³ = (a + b) (a² − ab + b²)<span> _________________________________ x</span>³ + 8 can be written as x³ + 2³ ; since 2³ = 8 ______________________________ So, using the formula: _____________________ a³ + b³ = (a + b) (a² − ab + b²) ; ______________________________ x³ + 8 ; or, x³ + 2³ ; can be factored; where a = x and b = 2. __________________________________ → Substitute these values for "a" and "b"; and rewrite: __________________________________ → x³ + 2³ = (x + 2) (x² - x*2 + 2²) ; __________________________________ → Simplify, and rewrite as: __________________________________ →x³ + 8 = x³ + 2³ = (x + 2) (x² − 2x + 4) ; __________________________________ →which is our first answer choice, "[A]". _________________________________________
