Download Adding and Subtracting Polynomials - MELT-Institute

Adding and Subtracting Polynomials
Using color pencils, color and label the following blocks to match those shown on the board. All red
tiles represent negative terms.
Just like real numbers, our algebra tiles may sum to zero.
3  3 
5   5 
99 
1. Color the tiles below to recreate the problem with algebra tiles. Sketch your problem and
solution below.
2
 3x  2 x  1   x 2  4 x  3
+
2. Using your algebra tiles, recreate this addition of polynomials. Show how you solved the
problem by sketching your tiles.
 2 x2  3x  5   4 x  2   _____________
The subtraction operation can be written as “addition of the opposite” just like when we work with real
numbers.
8  8  ___ and 8   8  ____
3. Likewise, subtraction of the polynomials can be rewritten as an addition problem.
 5x2  1   3x2  4 x  2  can be written as  ________    _____________  .
4. Using your algebra tiles, recreate this subtraction of polynomials. Show how you solved the
problem by sketching your tiles.
 5x2  1  3x2  4 x  2   __________________
5. When combining like terms, what part of each term changed? What stayed the same about each
term when you were adding or subtracting polynomials?
6. Although you do NOT have to sketch the tiles used to solve, complete the following using
algebra tiles. Pay close attention to whether you are adding or subtracting the polynomials.
 4x
2
x
2

 3   5 x  1  _______________
 

 2 x  3  2 x 2  3  _______________
 3x
2
 4x
 2 x   x  6   ______________
2

 x  2   3 x  2   ________________

7. Complete the following without algebra tiles. Show your work by lining up common terms.
 3x
2
7x
5x
 

 2 x  3  x 2  1  _______________
 

2
 6 x  3  9 x 2  x  3  _______________
2
 10 x  3  4 x 2  2 x  5  _______________
10 x
 
2


 7 x  9   5 x  9   _______________