Ex. 12. Required the product of a3 and -a3. Ans. -a. Ex. 13. Required the product of axz and bx2z. Ans. abx3z2. Ex. 14. Required the product of xyz and abc. Ex. 15. Required the product ·2a3bc2 d. Ans. -abcxyz. of -4bcd2 and Ans. 8a3b3c3d3. Ex. 16. Required the product of -3a3 and 4a. Ans. -12a4. 3 Ex. 17. Required the product of a2b3c by a2bc2d. Ans. a5b4c3d. 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 signs, will be the product required. Ex. 1. Multiply 4xy-3ax+2y proper Ex. 5. Multiply 8a2x2-3b+c by 2ac. Ans. 16a3cx2-6abc+2ac2. Ex. 6. Multiply -3x2-4a2+5 by -4ax. Ex. 7. Multiply a2+ax+x2 by ax. Ans. a3x+a2x2 + ax3. Ex. 8. Multiply x2-xy+y2 by —x2y. Ans. -x4y+x3 y2 — x2y3. Ex. 9. Multiply 3a -2ab+b2 by a2b2. Ans. 3a4b2-Ca3b3+3a2b4. Ex. 10. Multiply a2x2-ax+9 by 5. Ans. 5a2x2-5ax+45. Ex. 11. Multiply 2cd-3ab-3 by 4ac. Ans. 8ac2d-12a2bc-12ac. Ex. 12. Multiply 7xz+3ab-5y2 by ---xy. Ans. 7x2yz-3abxy+5xy3. Ex. 13. Multiply a+b-c-d by abcd. Ans. a2bcd+ab2cd-abc2d-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)× (a2+ab+b2)× (a2 —ab+b2). 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. Total prod. 2a* —7ba+7b2a3 + b3aa—15b1a3. a5 |