Adding polynomials with algebra tiles is the goal of this lesson. The learning 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 or the same and count them
You got a total of 5 light blue square tiles, so 5x^{2}
You got a total of 4 green rectangle tiles, so 4x
You got a total of 5 blue small square tiles, so 5
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
Keep this important fact in mind when adding polynomials
We call tiles that are alike or are the same type "like terms", so this means again that you can only add like terms
Basically, likes terms are terms with the same variable and the same exponent
For example, 2x^{2} and 5x^{2} are like terms because they have the same variable which is x and the same exponent which is 2.
To add like term, just add the coefficients, or the numbers attached to the term, or the number on the left side of the term
2x^{2} + 5x^{2} = (2 + 5)x^{2} = 7x^{2}
Example #2:
Add 6x^{2} + 2x + 4 to 10x^{2} + 5x + 6
Combine all like terms. You could use parentheses to keep things organized
(6x^{2} + 10x^{2}) + ( 2x + 5x) + (4 + 6)
Add the coefficient
(6 + 10)x^{2} + (2 + 5)x + 4 + 6
We get 16x^{2} + 7x + 10
Example #1: Done by combining like terms and adding the coefficients
Add 2x^{2} + 3x + 4 to 3x^{2} + x + 1
Combine all like terms. You could use parentheses to keep things organized
(2x^{2} + 3x^{2}) + ( 3x + x) + (4 + 1)
Add the coefficient
(2 + 3)x^{2} + (3 + 1)x + 4 + 1
We get 5x^{2} + 4x + 5
Notice that if the term is x, you can rewrite it as 1x, so your coefficient is 1