8

Ex. 12. Required the product of a3 and -a'.

Ans. --as. Ex. 13. Required the product of axz and bxoz.

Ans. abx3z Ex. 14. Required the product of -- xyz and abe.

Ans. - abcxyz. Ex. 15. Required the product of – 462cd2 and 2a3bc? d.

Ans. 8a3b3c3d3. Ex. 16. Required the product of – 3a’ and 4a.

-

Ans. --1294. Ex. 17. Required the product of ao b3c by a’bcod.

Ans. a564c3d.

с

с

CASE II.

When one factor is Compound and the other Simple.

RULE.

78. Multiply cach term of the compound factor by the simple factor, as in the last case; then these products placed one after another with their proper signs, will be the product required.

Ex. 1.
Multiply 4xy-3ax+2y

By 4ax

с

3

Ex. 5. Multiply 8a^ x2 --3b+c by 2ac.

Ans. 16u3cx2 - 6abc+2ac". Ex. 6. Multiply ---3.02 -- 4a+5 by --4ax.

Ans. 12ax 3 +16a" x — 20ax. Ex. 7. Multiply aż tax+x2 by ax.

Ans. a3x ta’xo + x . Ex. 3. Multiply 12 ----xy+ya by --x? y.

Ans. --*y+x?y? - yo. Ex. 9. Multiply 3a -- 2ub töb2 by a2b2.

Ans. 3a41,--Ca'b3 + 3uob*. Ex. 10. Multiply a??--ar+9 by 5.

Ans. 5a” 22

-59x +45. Ex. 11. Multiply 2cd-3ab--3 by fac.

Ans. Sac’d--12a2bc-12ac. Ex. 12. Multiply 7xz+- 3ab-5ya by ---xy.

Ans. -7xoyz-3abxy +5xy”. Ex. 13. Multiply a+b-c-d by abcd.

Ans. a'bcd+abcd-abcd-abcd2.

CASE III.
When both factors are compound quantities.

RULE.

79. Multiply every term of the multiplicand by each term of the multiplier successively as in the last case; then, add or connect all the partial products together, and the sum will be the product required.

Note. It is necessary to observe that like quantities are generally placed under each other, in order to facilitate their addition. And if several compound quantities are to be multiplied continually together; thus,

(a+b)x(a--b) X(a2 + ab + b2) X(ao-ab +-ba). Multiply the first factor by the second, and then that product by the third, and so on to the last factor; but it is sometimes more concise not to observe the order in which the compound quantities, or factors, are placed, as can be readily seen from the following examples.

EXAMPLE I.

Multiplicand 2a* -3ba3_-56ao
Multiplier a3 - 2ba2 + 3ba a

1st partial pro. 2a7-3ba-56%a5 second

-4bar +-662a5 +-106304 third

+-6b9a-9b3a4 - 1564a

3

Total prod. =2a-7ba® +76°25 + 63a4--1564a3.

="

1st partial prod. a ta'b-a3b3-a” 64 second,

-a5b-a4b2ta2b4 tabs third

ta4b2 ta3b3 -ab5-0

*

*

Total product ao

-69

Ex. 5.
Multiply az tab+62

by ao - ab +62

1st partial prod. a' ta'b+a262 second

-a3b-a2b2-ab3 third

ta'b' +-ab3-+-64

Ex. 6.
Multiply a* + a*b* +-64

by ao -

ist partial product a ta'ba +ao 14 second

-7% ma’b4-66

Total product

a6

*

-66

Ex. 7.
Multiply a tab+62

by a -6

1st partial prod. a' ta2b+aba second

-Q2b-ab2 63