Question

Which of the following expression is equivalent to the expression (y-x+3)(y-x-3) ?
a) y²-(x-3)²
b) (y-x)²-9
c) x²-(y+3)²

Answer 1

Answer:

(y-x)²-9 is equivalent to the expression (y-x+3)(y-x-3)

Step-by-step explanation:

First, solve given expression

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

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

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

= y² - xy - 3y - xy + x² + 3x + 3y - 3x - 9

Rearrange similar terms

=   x²+ y² - xy  - xy  - 3y  + 3y + 3x - 3x - 9

=   x²+ y² - xy  - xy  -9

=   x²+ y² - 2xy   -9

= (y -x)²- 9