How do you find the sum or difference of #(8y-4y^2)+(3y-9y^2)#?

When adding or subtracting you can not mix 'types' (variables)

#color(blue)("One method of several:")#

#8y-4y^2#
#ul(3y-9y^2) larr" add"#
#11y-13y^2#

#color(white)()#

#"+++++++++++++++++++++++++++++++++++"#
#"+++++++++++++ "color(blue)("Additional teaching")" +++++++++"#
#"+++++++++++++++++++++++++++++++++++"#

#color(brown)("When multiplying numbers if the signs are the same the answer is")##color(brown)("positive. If the signs are different the answer is negative.")#

Suppose that instead of adding the two brackets we had a subtraction.

#(8y-4y^2)-(3y-9y^2)#

Think of:
#(8y-4y^2)# as #+1(8y-4y^2)#

Multiply everything inside the bracket by +1 giving:

#8y-4y^2#
..........................................................................

Think of:
#-(3y-9y^2)# as #-1(3y-9y^2)#

Multiply everything inside #(3y-9y^2)# by -1 giving:

#-3y+9y^2#
.......................................................................
Sometimes it is helpful to think of add as 'put with' and subtract as 'remove from'

#ul("Putting")" it all together ( put with "-> +") we have:"#

#color(white)(..)8y-4y^2#
#ul(-3y+9y^2) larr" add"#
#color(white)(..)5y+5y^2#