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

please Give me an explanation for the correct answer.thanks

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3 Answers

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 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


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

(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.

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