Algebra Demystified 2nd Ed

138 algebra De mystif ieD

77 xy xy–=xy–= 17 xy()− 16 xy= xy

2

3

4 3

4

5

2

2

3

3

4

4 5

2

xx^22 –+yx+=xy  ++xx^2 –+ y=















88

12

9

12

8

2

5

2

 ++ (^2) +







xx− y
=^17
12
3
2
xx^2 – y
3 x^2 + 4xy – 8xy^2 – (2x^2 – 3xy – 4xy^2 + 6) = 3x^2 + 4xy – 8xy^2 – 2x^2 + 3xy + 4xy^2 – 6
= 3x^2 – 2x^2 – 8xy^2 + 4xy^2 + 4xy + 3xy – 6
= (3 – 2)x^2 + (–8 + 4)xy^2 + (4 + 3)xy – 6
= x^2 – 4xy^2 + 7xy – 6
PRACTICE
Combine like terms.

1. 3xy + 7xy =


2. 4x^2 − 6x^2 =


3. –+^3 =
   5

xy^222 xy

4. 8 xx  –  =


5. 2xy^2 − 4x^2 y − 7xy^2 + 17x^2 y =


6. 14x + 8 − (2x − 4) =


7. 16x−4 + 3x−2 − 4x + 9x−4 − x−^2 + 5x − 6 =
   8.^57 xy++xy^13 ––()xy^74 xy+=^


8. x^2 y + xy^2 + 6x + 4 − (4x^2 y + 3xy^2 − 2x + 5) =

✔SOLUTIONS

1. 3xy + 7xy = (3 + 7)xy = 10xy


2. 4x^2 − 6x^2 = (4 − 6)x^2 = − 2x^2


3. –^3 +=– +=– +=
   5

2 3

5

2 3

5

10

5

7

5

xy^22 xy  xy^22 xy x















yy^2

4.^88 xx–=()–=^17 xx
5. 2xy^2 − 4x^2 y − 7xy^2 + 17x^2 y = 2xy^2 − 7xy^2 − 4x^2 y + 17x^2 y
= (2 − 7)xy^2 + (−4 + 17)x^2 y
= −5xy^2 + 13x^2 y

PRACTICE

Combine like terms.