Question

(x-y) and (x² +y²+ xy) find the product​

Answer 1

Answer:

x³ - y³

Step-by-step explanation:

Given : (x - y)(x² + y² + xy)

We can write this as :

→ x(x² + y² + xy) - y(x² + y² + xy)

→ x(x²) + x(y²) + x(xy) - y(x²) - y(y²) - y(xy)

→ x³ + xy² + x²y - x²y - y³ - xy²

Writing the common terms together.

→ x³ + xy² - xy² + x²y - x²y - y³

→ x³ - y³

It is also an identity, which is as follows :

• a³ - b³ = (a - b)(a² + b² + ab)

Other similar identities which are frequently used are :

• a³ + b³ = (a + b)(a² + b² - ab)

• (a + b)³ = a³ + b³ - 3a²b + 3ab²

• (a - b)³ = a³ - b³ - 3a²b + 3ab²

Answer 2

Answer:

(x-y)(x²+y²+xy)

=x(x²+y²+xy)-y(x² +y²+ xy)

=x³+xy²+x²y-yx²-y³-xy²

=x³-y³

We know that,

☆(a³-b³)=(a-b)(a²+ab+b²)

☆(a³+b³)=(a+b)(a²-ab+b²)