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mariarad [96]
3 years ago
13

Expand the expression: a) (u + v)^3 b) (u + v)^4

Mathematics
1 answer:
MakcuM [25]3 years ago
8 0

Answer:

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

(b) (u^2+v^2+2uv )(u^2+v^2+2uv)=u^4+u^2v^2+2u^3v+u^2v^2+v^4+2uv^3+2u^3v+2uv^3+4u^2v^2=u^4+v^4+4u^3v+4v^3u+5u^2v^2                        

Step-by-step explanation:

We have to expand the expression

(a) (u+v)^3 there are different methods for expanding the expression here u used algebraic identity for expansion

We know the algebraic identity

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

(b) (u+v)^4

We know the algebraic identity (a+b)^2=a^+b^2+2ab

(u+v)^4 can be written as (u+v)^2\times (u+v)^2

(u^2+v^2+2uv )(u^2+v^2+2uv)=u^4+u^2v^2+2u^3v+u^2v^2+v^4+2uv^3+2u^3v+2uv^3+4u^2v^2=u^4+v^4+4u^3v+4v^3u+5u^2v^2

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Answer:

The sum of the first 37 terms of the arithmetic sequence is 2997.

Step-by-step explanation:

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The general rule of an arithmetic sequence is the following:

a_{n+1} = a_{n} + d

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We can expand the general equation to find the nth term from the first, by the following equation:

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