please give me a right solution for (a+b)^4

Question

please Give me an explanation for the correct answer.thanks

Answer 1

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

Answer 2

(a = b)^4 is the same as (a + b)(a + b)(a + b)(a + b) carrying out the first product (a^2 + 2ab + b^2)(a + b)(a + b) and keep going (a^3 + 2(a^2)b + ab^2 + ba^2 + 2ab^2 + b^3)(a + b) or (a^3 + 3ba^2 + 3ab^2 + b^3)(a + b) Just carry out the last multiplication being careful with the terms and you will get the expansion. Although this form isn't exactly simpler.

Answer 3

(a + b)^4 = a^4 + 4a^3b + 6a^2b^2 + 4ab^3 + b^4