Question

Hi friends new here can u answer this question?

The factors of x³ - x²y - xy² + y³ are?

Answer 1

x^3 - x^2y - xy^2 + y^3

=x^2(x-y) - y^2(x-y)

=(x-y)(x^2 - y^2)

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

=(x-y)^2 (X+y)

Answer 2

Question: x³ - x²y - xy² + y³

Solution:

$\red{ \sf{ \implies{x {}^{3} - x {}^{2} y + y {}^{3} - xy {}^{2}}}} \\ \\ \green{ \sf{ \implies{ x {}^{3} - x {}^{2} y - xy {}^{2} + y {}^{3}}}} \\ \\ \red{ \sf{ \implies{x {}^{2} (x - y) - y {}^{2} (x - y)}}} \\ \\ \implies{\blue{ \sf{ (x - y)(x {}^{2} - y {}^{2} )}}} \\ \\ \implies{ \green{ \sf{ (x - y)(x - y)(x + y)}}}\\ \\ \: \pink{ \sf{ \implies(x - y) {}^{2} (x + y)}} \\ \\ \red{ \sf{ \implies( x {}^{2} - 2xy + y {}^{2} )(x + y)}}$

Important Algebraic identities:

→ a³ - b³ = ( a - b)(a²+ ab + b²)

→ a³ + b³ = ( a + b)(a² - ab + b²)

→ a² - b² = (a+b)(a-b)

→ (a+b)² = a² + b² + 2ab

→ (a- b)² = a² + b² - 2ab