Page:Elementary algebra (1896).djvu/51

33 Rh 49. We shall now give a few examples of greater difficulty.

Ex. 1. Find the product of 3x^2 —2x —5 and 2x— 5.

Each term of the first expression is multiplied by 2x, the first term of the second expression ; then each term of the first expression is multiplied by — 5; like terms are placed in the same columns and the results added.

Ex. 2. Multiply a—b+3c by a+2b

a- b+3c a+ 2b a^2— ab+3ac 2ab — 2b^2 + 6bc

a+ ab+3ac— 2b^2+6bc

When the coefficients are fractional, we use the ordinary process of Multiplication, combining the fractional coefficients by the rules of Arithmetic.

Ex. 3. Multiply 1a^2 — ab +2b^2 by 4a+4 b.

1a^2— ab + 30b^2 2a + b 2a^3— 4a^2b + ab^2 + a^2b — tab^2 + 2b^3 a^3 — a^2b + ab^2 + 3b^3

50. If the expressions are not arranged according to powers ascending or descending of some common letter, a rearrangement will be found convenient.

Ex. Multiply 2xz —2z^2+2x^2-3yz+ xy by x—y+2z.

227+ xy +2uz—3yz2-—2

ee 2034 gy 42972 —Baxyz— x2? — 227y — 2ayz —apP+3y2+ yz 4a2z + Qryz +402? —6y22-22

2038 — oy + 6222 — Bayz + 8x2? — xy? + 3 yz — Syz? 228 D