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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