CASE III.

To add quantities which are unlike, and have unlike signs.

RULE.

Collect all the like quantities together by the last rule, and set down those that are unlike, one after another, with their proper signs.

SUBTRACTION.

RULE.

Change the signs of all the quantities to be subtracted, or conceive them to be changed, and then collect the different terms together as in addition.

5x2y-8 4√xy-xxy

-3x2y +1 2✓xy+2+xy 6x2-1046 x 2

5x2+x-8-40

3xy--20

4x33.(a+b)

xy3+10a (xy+10)

4xy-30 3x2 8.(a+b).

x2y2+2a√(xy+10)

MULTIPLICATION.

CASE I.

When both the factors are simple quantities.

RULE.

Multiply the co-efficients of the two terms together, and to the product affix all the letters in those terms, and the result will be the whole product required. Note*. Like signs produce +, and unlike signs

* That like signs make +, and unlike signs, in the product,

may be shown thus:

1st. When

a is to be multplied by +b: this implies that a

CASE II.

When one of the factors is a compound quantity.

RULE.

Find the products of the multiplier, and every term of the multiplicand, separately, and place them one after another, with the proper signs, and the result will be the whole product required.

is to be taken as many times as there are units in b; and, since the sum of any number of affirmative terms is affirmative, it is plain tha (+a)×(+b)=+ab.

2. If two quantities are to be multiplied together, the resul will be exactly the same, in whatever order they are placed for a times b is the same as b times a; and, therefore