Question

How do you factor `16-(y-3)^2`?

Answer 1

(7 -y)(1 +y)

Explanation:

This expression is a `color(blue)"difference of squares"` which, in general factorises as.

`color(red)(|bar(ul(color(white)(a/a)color(black)(a^2-b^2=(a-b)(a+b))color(white)(a/a)|))) ........ (A)`

Now `16=4^2rArra=4" and " (y-3)^2rArrb=y-3`

Substitute these values for a and b into (A)

`rArr16-(y-3)^2=(4-(y-3))(4+y-3)`

Simplifying the brackets gives.

`(4-y+3)(1+y)=(7-y)(1+y)`

`rArr16-(y-3)^2=(7-y)(1+y)`