Adding and Subtracting Polynomials Notes
Unit 1D Polynomials (Adding/Subtracting)
Distributing: Multiplying everything inside the ( ) by what is outside.
If there is -# in front of the ( ) then change the sign of everything inside the ( ).
- ( ) is the same as -1( )
Example 1:
a) 3(x2 + 2x – 1) (b) -2(x2 – 4x – 3) (c) -1(4x + 2) (d) - (x – 3) ( -1(x – 3)
3x2 + 6x – 3 -2x2 + 8x + 6 -4x – 2 -1x + 3
Adding/Subtracting: Add (or subtract) coefficients of same variable with same exponent.
Example 2:
a) 5x2 + 3x + 2x2 – 7x (b) 2x3 + 5x2 – 3x + 2 -11x (c) -5x3 + 2y3 – 7x3 - 2y
5x2 + 2x2 +3x – 7x 2x3 + 5x2 – 3x – 11x + 2 -5x3 – 7x3 + 2y3 – 2y
7x2 – 4x 2x3 + 5x2 – 14x + 2 -12x3 + 2y3 – 2y
Using ( ). Distribute and then add like terms
Example 3: Simplify.
(a) [pic] (b) 3(x2 + 2x) – 2(x + 3) c) 4(x -2) – (x – 3) – 2(x2+ 4)
1(12m2 + 4) + 1(8m2 + 5) 3x2 + 6x – 2x - 6 mult by -1 mult by -2
12m2 + 4 + 8m2 + 5 3x2 + 4x – 6 4x – 8 - x + 3 – 2x2 - 8
12m2 + 8m2 + 4 + 5 -2x2 + 4x – x – 8 + 3 - 8
20m2 + 9 -2x2 + 3x – 13
Perimeter: Write down all sides and then add the sides to find perimeter. If perimeter is missing then subtract each side from perimeter
Example 4
(a) (b) Perimeter = 8x + 15
Missing sides: 6, 3x + 5 Answer: 8x + 15 – (-9) – (3x + 5)
6 + 6 + 3x + 5 + 3x + 5 8x + 15 + 9 – 3x - 5
3x + 3x + 5 + 5 + 6 + 6 5x + 19
6x + 22
Practice 1-7: Determine if the following are correct or incorrect. If it is incorrect then show the correct steps and correct answer.
1) 2x – 3x + 5x2 2) 3x + 4x2 3) - (x + 7) 4) 2(x – 3) – (x + 4)
-x + 5x2 7x2 - x – 7 2x – 6 – x - 4
2x – x – 6 - 4
x + 10
5) 2(x – 3) -3(x + 2) 6) 4(x2 + 2x) – (x – 3) 7) The perimeter is 12x + 9. Find the missing side.
2x – 6 – 3x – 6 4x2 + 8x –x + 3 12x + 9 – (6) – (2x – 7)
2x – 3x – 6 – 6 4x2 + 7x + 3 12x + 9 – 6 – 2x + 7
- x – 12 10x + 10
8-18) Simplify.
8) 2(x – 3) – 5(x + 2) 9) –(x + 7) + 2(x + 3) 10) 8(x – 4) – (x + 2) 11) 4x2 – 3x – 2x2 – 7x + 1
12) 8(x +1) – 3(x – 6) 13) 5x – 3 – (x + 1) 14) 7x2 – 5x -3(x + 4) 15) 8(x – 3) – (x + 7)
16) [pic] 17) [pic] 18) [pic]
19- 21) Find the perimeter
19) 20) 21)
22) Find the perimeter of a square whose side is equivalent to (5x – 3).
23-24) The perimeter is given. Find the length of the missing side
23) 24) Perimeter: 18x + 10
Perimeter: 16x + 10
-----------------------
6
3x+5
-9
3x+5
6
2x-7
x+3
6
10
x-9
x+3
3x+5
8
3x+5
2x-7
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