The sum of two polynomials is #10a^2b^2-9a^2b+6ab^2-4ab+2#. If one addend is #-5a^2b^2+12a^2b-5#, what is the other addend?

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Answer 1 · 2017-08-27T18:41:08

See a solution process below:

Let's call the second addend: #x#

We can then write:

#x + (-5a^2b^2 + 12a^2b - 5) = 10a^2b^2 - 9a^2b + 6ab^2 - 4ab + 2#

To find the second addend we can solve for #x#:

#x + (-5a^2b^2 + 12a^b - 5) - (-5a^2b^2 + 12a^2b - 5) =#
#10a^2b^2 - 9a^2b + 6ab^2 - 4ab + 2 - (-5a^2b^2 + 12a^2b - 5) #

#x + 0 = 10a^2b^2 - 9a^2b + 6ab^2 - 4ab + 2 + 5a^2b^2 - 12a^2b + 5#

#x = 10a^2b^2 - 9a^2b + 6ab^2 - 4ab + 2 + 5a^2b^2 - 12a^2b + 5#

We can now group and combine like terms:

#x = 10a^2b^2 + 5a^2b^2 - 9a^2b - 12a^2b + 6ab^2 - 4ab + 2 + 5#

#x = (10 + 5)a^2b^2 + (-9 - 12)a^2b + 6ab^2 - 4ab + (2 + 5)#

#x = 15a^2b^2 + (-21)a^2b + 6ab^2 - 4ab + 7#

#x = 15a^2b^2 - 21a^2b + 6ab^2 - 4ab + 7#