Adding polynomials by combining like terms together and using algebra tiles is the goal of this lesson. We will show you the following three ways to add polynomials.
We will start with algebra tiles since the process is a lot more straightforward and concrete with tiles. To this end, study the model below with great care.
Example #1:
Add 2x^{2} + 3x + 4 and 3x^{2} + x + 1
Step 1
Model both polynomials with tiles.
Step 2
Combine all tiles that are alike and count them.
Putting it all together, we get 5x^{2} + 4x + 5
I hope from the above modeling, it is clear that we can only combine tiles of the same type. For example, you could not add light blue square tiles to green rectangle tiles just like it would not make sense to add 5 potatoes to 5 apples. Try adding 5 potatoes to 5 apples and tell me if you got 10 apples or 10 potatoes. It just does not make sense!
Example #2:
Add 2x^{2} + -3x + -4 and -3x^{2} + -x + 1
Step 1
Model both polynomials with tiles
Step 2
Combine all tiles that are alike and count them. Tiles that are alike, but have different colors will cancel each other out. We show each cancellation with a green line.
Putting it all together, we get -x^{2} + -4x + -3
Example #3:
Add 6x^{2} + 8x + 9 and 2x^{2} + -13x + 2
Line up like terms. Then add the coefficients.
6x^{2} + 8x + 9
+ 2x^{2} + -13x + 2
------------------------------
8x^{2} + -5x + 11
Example #4:
Add -5x^{3} + 4x^{2} + 6x + -8 and 3x^{3} + -2x^{2} + 4x + 12
Line up like terms. Then add the coefficients.
-5x^{3} + 4x^{2} + 6x + -8
+ 3x^{3} + -2x^{2} + 4x + 12
--------------------------------------
-2x^{3} + 2x^{2} + 10x + 4
Example #5:
Add 6x^{2} + 2x + 4 and 10x^{2} + 5x + 6
Combine or group all like terms. You could use parentheses to keep things organized.
(6x^{2} + 2x + 4) + (10x^{2} + 5x + 6) = (6x^{2} + 10x^{2}) + (2x + 5x) + (4 + 6)
(6x^{2} + 2x + 4) + (10x^{2} + 5x + 6) = (6 + 10)x^{2} + (2 + 5)x + (4 + 6)
Add the coefficient
(6x^{2} + 2x + 4) + (10x^{2} + 5x + 6) = 16x^{2} + 7x + 10
Example #6:
Add 2x^{4} + 5x^{3} + -x^{2} + 9x + -6 and 10x^{4} + -5x^{3} + 3x^{2} + 6x + 7
(2x^{4} + 5x^{3} + -x^{2} + 9x + -6) + (10x^{4} + -5x^{3} + 3x^{2} + 6x + 7)
= (2x^{4} + 10x^{4}) + (5x^{3} + -5x^{3}) + (-x^{2} + 3x^{2}) + (9x + 6x) + (-6 + 7)
= (2 + 10)x^{4} + (5 + -5)x^{3} + (-1 + 3)x^{2} + (9 + 6)x + (-6 + 7)
= (12)x^{4} + (0)x^{3} + (2)x^{2} + (15)x + (1)
= 12x^{4} + 2x^{2} + 15x + 1
Notice that if the term is x^{2}, you can rewrite it as 1x^{2}, so your coefficient is 1. We did this in example #6, third line with (-x^{2} + 3x^{2})
(-x^{2} + 3x^{2}) = (-1x^{2} + 3x^{2})
Mar 29, 23 10:19 AM
Mar 15, 23 07:45 AM