(x + y) - (x + y)^2 + (x + y)^3
please factorise this
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EXPLANATION.
Factorizes.
⇒ (x + y) - (x + y)² + (x + y)³.
As we know that,
Formula of :
⇒ (a + b)² = a² + b² + 2ab.
⇒ (a + b)³ = a³ + 3a²b + 3ab² + b³.
Using this formula in the equation, we get.
⇒ (x + y) - (x² + y² + 2xy) + (x³ + 3x²y + 3xy² + y³).
⇒ x + y - x² - y² - 2xy + x³ + 3x²y + 3xy² + y³.
⇒ x³ + y³ - x² - y² + 3x²y + 3xy² + x + y - 2xy.
⇒ (x³ + 3x²y - x²) + (y³ + 3xy² - y²) + x + y - 2xy.
⇒ x²(x + 3y - 1) + y²(y + 3x - 1) + x + y - 2xy.
MORE INFORMATION.
Important formula.
(1) (a + b)² = a² + b² + 2ab.
(2) (a - b)² = a² + b² - 2ab.
(3) (a² - b²) = (a + b)(a - b).
(4) (a² + b²) = (a + b)² - 2ab.
(5) (a³ + b³) = (a + b)(a² - ab + b²).
(6) (a³ - b³) = (a - b)(a² + ab + b²).
(7) (a + b)³ = a³ + 3a²b + 3ab² + b³.
(8) (a - b)³ = a³ - 3a²b + 3ab² - b³.
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