Until you get used to them it seems quite tricky to multiply out brackets.
Using color to show what is happening.
Given: y=color(blue)((x-3))color(brown)((x-4))
You can split the multiplication up into parts like this:
y=color(blue)(xcolor(brown)((x-4))-4color(brown)((x-4)) ..........(1)
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color(blue)("Using numbers to explain what is happening")
This is a bit like: 3xx4 =12
Now mater how we split the 3 we will always end up with 12
color(brown)((1+2)color(blue)(xx4)
=color(brown)((1color(blue)(xx4))+(2color(blue)(xx4))
color(blue)(4+4+4)color(white)(.)= 12
It will even work if you write 3 as 4-1
color(brown)((4-1))color(blue)(xx4)
color(brown)((4color(blue)(xx4))-(1color(blue)(xx4)) the last bracket gives you color(green)(-4)
color(blue)(4+4+4+4color(green)( -4)) =12
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color(red)("Back to your question")
So equation (1) becomes:
y=(x^2-4x)color(red)(-)(color(green)(+4x-16)).........(2)
As there is no multiplication left we can removing the brackets
y=x^2-4xcolor(green)(color(blue)(bb-)4xcolor(blue)(+)16)......................(3)
Notice the way the color(red)("minus sign")color(white)(.) underline("outside") the underline("last") bracket in equation (2) changes all the color(blue)("signs inside") it when the bracket is removed. Giving equation (3)
y=x^2-8x+16
