Question

factorise x²-y²+6y-9​

Answer 1

x²-y²+6y-9

= x² - (y²-6y+9)

= x² - (y²-2*x*3+3²)

= x²- (y-3)²

= [x+(y-3)][x-(y-3)]

= (x+y-3)(x-y-3)

Answer 2

Step-by-step explanation:

There are two solution

1) x

$x { }^{2} - y ^{2} + 6y - 9$

$= x { }^{2} - 9 - y {}^{2} + 6y$

$= x {}^{2} - 3 {}^{2} - y {}^{2} + 6y$

$= (x {}^{2} - 3 {}^{2} ) - y(y - 6)$

$= (x + 3)( x - 3) - y(y - 6)$

solution fisrt

2)

$x {}^{2} - y {}^{2} + 6y - 9$

$x {}^{2} - (y {}^{2} - 6y + 9)$

$= x {}^{2} - (y {}^{2} - 2 \times 3 \times y + 3 {}^{2} )$

$= x {}^{2} - (y - 3) {}^{2}$

$= (x + y - 3)(x - y + 3)$

second solution