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\huge\text{\bold{Question:}}

Could anyone please help me with my homework? Thanks in advance! :)

\huge\bold{(x+2)^(3) }
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User Vadimchin
by
6.7k points

2 Answers

11 votes

Given:


(x + 2)^(3)

Now using algebraic identities,


{x}^(3) + 3(x)^(2) + 3(x)(2)^(2) + {2}^(3)


= > {x}^(3) + 3(x)^(2) + 3(x)(2)^(2) +8


= > {x}^(3) + 6x^(2) +12x +8

~ Benjemin360

User Sisyphe
by
6.0k points
5 votes

Solution:

  • Before you solve this question, remember this identity of the cube of a binomial.


(a + b) ^(3) = {a}^(3) + {b}^(3) + 3ab(a + b) \\

  • Here, we have to find the cube of (x + 2).
  • Replacing a by x and b by 2 in the above identity, we have


(x + 2) ^(3) \\ = {(x)}^(3) + (2) ^(3) + 3 * x * 2(x + 2) \\ = {x}^(3) + 8 + 6x(x + 2) \\ = {x}^(3) + 8 + 6x * x + 6x * 2 \\ = {x}^(3) + 8 + {6x}^(2) + 12x

  • Now, arrange the above expression in standard form.


= {x}^(3) + {6x}^(2) + 12x + 8 \\

Answer:


{x}^(3) + {6x}^(2) + 12x + 8

Hope you could understand.

If you have any query, feel free to ask.

User Micah Armantrout
by
6.1k points
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