please Give me an explanation for the correct answer.thanks

Just to add my two cents worth...which really isn't that much.. :( your could do as above...with the first answer....another way might be to begin: (a + b)^4 the quantity a plus b to the 4th power take (a + b)^2 times (a + b)^2 with (a + b)^2 = a^2 + 2ab + b^2 (a + b)^2 times (a + b)^2 = (a^2 + 2ab + b^2)(a^2 + 2ab + b^2) now multiply each of the expressions in each trinomial, keeping like terms in line to keep from getting confused: a^2 (a^2 + 2ab + b^2) = a^4 + 2a^3 b + a^2 b^2 2ab (a^2 + 2ab + b^2) = 2a^3 b + 4a^2 b^2 + 2ab^3 b^2 (a^2 + 2ab + b^2) = a^2 b^2 + 2ab^3 + b^4 now add all three together under like-terms a^4 + 4a^3 b + 6a^2 b^2 + 4ab^3 + b^4 I have my students do it this way...it is less confusing...the important things to remember is keep all like-terms in alignment AND the more you do these kinds of problems...the easier they will get and the better you'll get at doing these kinds of problems

## Comments

Thank you very much for the help Mr John G. appreciate you.your students are lucky!