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GREATEST COMMON MEASURE.

Proceed as in Arithmetic, or split up into factors. 1. 3x2y2 + 6x2y3 = 3xy2 (x + 2xy) and 12xy? + 9x2y2 = 3xy2 (4+3x) = 3xy3.

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Taking out factor 3x=x+1) 3+1 (x2-x+1

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5 tỏ -x+1) x2-6x+5 (−x+5

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6. 8.-8

7.

=(2x-2) 4

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} 2x-2

Ga2-18x+12= (2x-2) (3x-6) j

8u3+863 and 12a2-24ab-3662 4 (2a3+2b3) 4 (3a2-6ab-962)

3a2-6ab-9b2) 12a3+12b3 (4a+8b

12a3-24a2b-36ab2

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8. 4a3y2-8a2y3 and 2a2y2 (2a-4y)

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12a3y3+6a+y3 2ay (6a3y +3a3y

= 2a2y2

9. (+) and 5-4-23 (x2+x)2 == x2+2x3+23 Then x+2x+x2) æ3—æ±—2æ3 (x-3

-x

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-6x+11x+21) 6.x2+6a2-54e-54

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·x3-42-25x+28_ (x−7) (x2+3x-4)
and 22-14+49 (x-7) (x-7)

=

12.

x2+10x2+25x−28 _ (x+7) (x2+3x+4) Į and x2+14x+49 (x+7) (x+7)

13. x3-9x2+15x

=

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}

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=x+7

=x--2

(a+5) (a-1)) =a2+4a-5 = (a+5) (a+2)

(a+5) (a-5)=a2-25

15.

(a+1) (a2-a+1)

=a2 +7a−10

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(x+1) (a2+ab-a+1)

a2-3x+2, a2—a—
2 and a2-4a+4

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(a-2) (a-1))

= (a−2) (a+1)
(a-2) (a-2))

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Having explained the four simple rules in Algebra, we will now proceed to Simple Equations in which these may be worked out.

An Equation is an expression in Algebra consisting of two portions united by the sign =, such that the quantity on the one side is the same in numerical value as the other, as x+b=7.

If this equation contain an unknown in the 1st power, that is not the square, cube, &c., it is called a Simple Equation, as a+a=17.

As the two halves of the equality, united by =, are equal, the equality will not be destroyed by adding, subtracting, multiplying, or dividing, provided we do the same to both sides of the equation. Thus if x + a = 7, then x + a +3=7+3, and a + a 3 7-3, and 4 (x + a) = 4 × 7 or x + a 7

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3. x+c=24+c a=24 4. 2x+2=6

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-18=10x 48x-3x-72=40x x=143

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10.

8

4

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II.

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12. 4ax + 26 = 6cx+8a

25x+210=36x+78 x=12

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4x

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x=

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