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
