SOLUTION: Use the Binomial Theorem to expand the binomial and express the result in simplified form. (x + 4)3

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Question 1172645: Use the Binomial Theorem to expand the binomial and express the result in simplified form. (x + 4)3
Found 3 solutions by ewatrrr, MathTherapy, ikleyn:
Answer by ewatrrr(24785) About Me  (Show Source):
You can put this solution on YOUR website!


Hi  

%28a%2Bb%29%5E3+=+a%5E3+%2B+3a%5E2b+%2B+3ab%5E2+%2B+b%5E3

a = x  and b = 4

Might be best to start as below.. to eliminate any sloppiness

(x + 4)^3 = x^3 + (3)(b)x^2 + 3(b^2)x + 64



(x + 4)^3 = x^3 + (3)(4)x^2 + 3(16)x + 64

(x + 4)^3 = x^3 + 12x^2 + 48x + 64

We all most heartedly agree that is the correct response.

Wish You the Best in your Studies.

Answer by MathTherapy(10552) About Me  (Show Source):
You can put this solution on YOUR website!
Use the Binomial Theorem to expand the binomial and express the result in simplified form. (x + 4)3
(x + 4)3 should be (x + 4)3

 <====== Binomial Expansion Formula

In this case, there are 4 terms, so we get:



There're only 4 terms so it's quite easy to EXPAND the binomial, in order to check this answer!

Answer by ikleyn(52788) About Me  (Show Source):
You can put this solution on YOUR website!
.

            The post by  @ewatrrr contains  FATAL  ERRORS.

            I came to bring you the  CORRECT  SOLUTION. 


 
%28a%2Bb%29%5E3 = a%5E3 + 3a%5E2b + 3ab%5E2 + b%5E3

(x + 4)^3 = x^3 + (3)(4)x^2 + 3(16)x + 64

(x + 4)^3 = x^3 + 12x^2 + 48x + 64.

Solved.


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In my young years,  when I studied at the middle school,  one of many requirements
of our educational program in  Math  was to know such identities as the multiplication table.


                    As   2 x 2 = 4.


/\/\/\/\/\/\/\/\/

Since you do not know these basic issues, look into the lessons


1. The cube of the sum formula is                 %28a+%2B+b%29%5E3+=+a%5E3+%2B+3a%5E2%2Ab+%2B+3a%2Ab%5E2+%2B+b%5E3.
      For details and examples of applications of this formula see the lesson The cube of the sum formula.


2. The cube of the difference formula is     %28a+-+b%29%5E3+=+a%5E3+-+3a%5E2%2Ab+%2B+3a%2Ab%5E2+-+b%5E3.
      For details and examples of applications of this formula see the lesson The cube of the difference formula.


3. The sum of cubes formula is                       a%5E3+%2B+b%5E3+=+%28a+%2B+b%29%2A%28a%5E2+-+ab+%2B+b%5E2%29.
      For details and examples of applications of this formula see the lesson The sum of cubes formula.


4. The difference of cubes formula is           a%5E3+-+b%5E3+=+%28a+-+b%29%2A%28a%5E2+%2B+ab+%2B+b%5E2%29.
      For details and examples of applications of this formula see the lesson The difference of cubes formula.


Learn the subject from there   (as the multiplication table).