Factoriser 1-9x²-y²-6xy

(1 - 3x - y) (1 + 3x + y)

Step-by-step explanation:

Given

1 - 9x² - y² - 6xy

= 1 - (9x² + y² + 6xy) ← perfect square

= 1 - (3x + y) ²

1 - (3x + y) ² is a difference of squares and factors in general as

a² - b² = (a - b) (a + b)

Here a = 1 and b = 3x + y, thus

1 - (3x + y) ²

= (1 - 3x - y) (1 + 3x + y) ← in factored form

- (1+3x+y) (3x+y-1)