Question

find the expansion of the following :
(x+y+2)^3​

Answer 1

Answer:

x

3

−

y

3

−

3

x

2

y

+

3

x

y

2

Explanation:

(

x

−

y

)

3

=

(

x

−

y

)

(

x

−

y

)

(

x

−

y

)

Expand the first two brackets:

(

x

−

y

)

(

x

−

y

)

=

x

2

−

x

y

−

x

y

+

y

2

⇒

x

2

+

y

2

−

2

x

y

Multiply the result by the last two brackets:

(

x

2

+

y

2

−

2

x

y

)

(

x

−

y

)

=

x

3

−

x

2

y

+

x

y

2

−

y

3

−

2

x

2

y

+

2

x

y

2

⇒

x

3

−

y

3

−

3

x

2

y

+

3

x

y

2

Always expand each term in the bracket by all the other terms in the other brackets, but never multiply two or more terms in the same bracket.

Answer 2

(x+y+2)^3

=> x^3+y^3+2^3+ (x+y+2)(xy+2y+2x)

=>x^3+y^3+8+ (x+y+2)(xy+2y+2x)

Cheers!