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

Question

Ethan Adkins · Accepted Answer

#11y-13y^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#

Eva Abramson · Answer

undefined To find the sum or difference of (8y-4y^2)+(3y-9y^2), first combine like terms:

(8y - 4y^2) + (3y - 9y^2) = (8y + 3y) + (-4y^2 - 9y^2)

= 11y - 13y^2

Kennedy Adams · Answer

undefined To find the sum or difference of $(8y - 4y^2) + (3y - 9y^2)$, combine like terms:

$$ (8y - 4y^2) + (3y - 9y^2) $$

Combine the terms with the same variables (y) together:

$$ (8y + 3y) + (-4y^2 - 9y^2) $$

$$ 8y + 3y = 11y $$

$$ -4y^2 - 9y^2 = -13y^2 $$

So, the sum of $(8y - 4y^2) + (3y - 9y^2)$ is $11y - 13y^2$.