Alegebraic Equations

Textbook- Page 40/ exercise 1a

16/54= 8/27 (the common factor is 2)                 Harder:

5a/25=a/5 (the common factor is 5)                     4/12x= 1/3x

21xy/7x=3y (the common factor is 7x)               3pq/6p= q/2

                                                                           10x/15xy= 2/3y

Examples:

• Simplify 3x (x-y)/x-y = 3x (the 2 "x-y" cancel each other out, leaving 3x)
• Simplify 5a(a+b)/(a+b)(a-b) = 5a/a-b (the 2 "a{+=b" cancel each other out, leaving 5a/a-b)
• Simplify a-b/3(a=b) = This cannot be simplified due to no common factor. We write this as "NSF"
• Simplify 5+6/(5+6)(5-6) = 1/5-6
• x+y/2(x-y) = NSF

1.x2-7x-18 = (x-2)(x-9)

2.x2+15x+26 = (x+2)(x+13)

3.x2-20x+96 = (x-12)(x-8)

4.y2+18y-40 = (y+20)(y-2)

5.x2+13x+22 = (x+11)(x+2)

6. y2-21y-100 = (y+4)(y-25)

7.x2-9 = (x-3)(x+3)

8.x2-121 = (x-11)(x+11)

9.x2-144 = (x-12)(x+12)

a) -(x-2) = -x+2

b)-(x-3) = -x+3

c)-(2x-1) = -2x+1

d)-(x-5) = -x+5

Generally:       -(a-b)=-b-a

                        -(b-a) = a-b

It follows a-b/b-a and b-a/a-b