Question

Find the factor of :-
( x + y )³ - ( x³ + y³ )​

Answer 1

Answer:

Solution :-

✪ (x + y)³ - (x³ + y³)

➻ {(x)³ + 3 × x² × y + 3 × x × y² +(y)³} - (x³ + y³)

➻ {x³ + 3x²y + 3xy² + y³} - (x³ + y³)

➻ x³ + 3x²y + 3xy² + y³ - x³ - y³

➻ x³ - x³ + y³ - y³ + 3x²y + 3xy²

➻ 3x²y + 3xy²

➻ 3xy(x + y)

∴ The answer of this question is 3xy(x + y)

Answer 2

From the given question the correct answer is:

The answer of this question is 3xy(x + y)

Given:

( x + y )³ - ( x³ + y³ )​

To find:

Factor of given

Solution:

we have to find the factor of the ( x + y )³ - ( x³ + y³ )​

so we will go by step by step

(x + y)³ - (x³ + y³)

we know that,

(A+B) ³= A³ +B³ +3A 2 B+3AB

expand it

= {(x)³ + 3 × x² × y + 3 × x × y² +(y)³} - (x³ + y³)

= {x³ + 3x²y + 3xy² + y³} - (x³ + y³)

= x³ + 3x²y + 3xy² + y³ - x³ - y³

=x³ - x³ + y³ - y³ + 3x²y + 3xy²

= 3x²y + 3xy²

=3xy(x + y)

Hence, The answer of this question is 3xy(x + y)