Question

Complete the following identities (x+y)³

Answer 1

Step-by-step explanation:

What is the answer of (x+y)³?

By answer, I assume you mean the expanded form?

(x+y)3=(x+y)(x+y)(x+y)

taking the first two:

(x+y)(x+y)=x(x+y)+y(x+y)

=x2+xy+yx+y2

=x2+2xy+y2.

This gives us

(x+y)3=(x2+2xy+y2)(x+y)

this can be expanded out into:

x(x2+2xy+y2)+y(x2+2xy+y2)=x3+2x2y+xy2+yx2+2xy2+y3

this can be simplified into

x3+3x2y+3xy2+y3

so (x+y)3=x3+3x2y+3xy2+y3

There are quicker ways to do this but that requires more advanced concepts like Pascal’s triangle or the binomial theorem and it’s better to grasp the basics before moving on to more advanced topics.

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