Which term of the expansion contains x^10

Question

Which term of the expansion of (x²+2)⁸ contains x¹⁰?

the term number that contains x¹⁰ is?

Answer 1

Hey Dalia,

 

We can do this without computing the entire expansion.  Notice that the first term will have an (x^2)^8, the second will have (x^2)^7 or x^14, and so on.  Following this pattern, it will be the fourth term that will contain x^10 since (x^2)^5 = x^10.  Now, we found the term number, but need the complete term to answer the first question asked.  I'm assuming you have the formula for the expansion, but the example at the bottom of the page, http://www.purplemath.com/modules/binomial.htm, can be used as a guide.

The complete term should look like, ((8C3)(x^2)^5)(2)^3 before being simplified.  I hope this helps!  

Answer 2

Dalia, see: http://www.wyzant.com/resources/answers/30919/what_is_the_term_number

 

In this post, Michael's answer is the same as mine, so we're probably right.

Answer 3

Dalia,

 

 

The binomial expansion :

 

Here is the expansion of (x + y)n for n = 0, 1,…, 5 :

(x + y)⁰ = 1

(x + y)¹ = x + y

(x + y)² = x ² +2xy + y ²

(x + y)³ = x ³ +3x ² y + 3xy ² + y ³

(x + y)⁴ = x 4 +4x ³ y + 6x ² y ² +4xy ³ + y ⁴

(x + y)⁵ = x ⁵ +5x ⁴ y + 10x ³ y ² +10x ² y ³ +5xy ⁴ + y ⁵

 

and it goes on like that

 

so in your situation

 

(x² + 8)⁸  =  (x²)⁸ ....

 

Try to expand it