...with Art. 99, the following principles are of great importance : If n is any whole number, (1) a" + b" is divisible by a + b if n is odd, and by neither...is odd, and by both a + b and a — b if n is even. EXAMPLES. 101. 1. Divide a7 - b'< bу ab. Applying the laws of Art. 99, we have ot 0 ,1 r, , , a-6...

...principles are of gre?«; importance : If n is any whole number, (1) a" 4 4" is divisible by a + bif n is odd, and by neither a + b nor a — b if n is...is odd, and by both a + b and a — b if n is even. EXAMPLES. 101. 1. Divide о7 — V by a — b. Applying the laws of Art. 99, we have 7 = a6 + cfb +...

...b" is divisible by a + b if n is odd, and by neither a + b nor a — b if n is even. (2) a" — bn is divisible by a — b if n is odd, and by both a + b and a — b if n is even. EXAMPLES. 101. 1. Divide a" - b' by о - b. Applying the laws of Art. 99, we have dV a — b = a6 +...

...following laws will enable one readily to do this : 1. The terms of the quotient, or second factor, are all positive when the divisor is a — b, and...alternately positive and negative when the divisor is a + b. 2. The number of terms always corresponds to the degree of the binomial. 3. a appears in the first...

...nor a — b if n is even. (2) a" — 6" is divisible by а — Ъ if n is odd, and by both ь + Ъ and a — b if n is even. NOTE. It is important to...the quotient are all positive when the divisor is a — 6, and alternately positive and negative when the divisor is a + b ; also, that the quotient is...

...Attention to the following laws will enable one readily to write out the factors of such expressions. 1. The terms of the quotient are all positive when the...alternately positive and negative when the divisor is a + b. 2. The number of terms corresponds to the degree of the binomial. 4. The exponent of a in the first...

...odd, and by neither a + b nor a — b if n is even. 174. It is seen from Formulas (2) and (4) m § 172 that the terms of the quotient are all positive when the divisor is a — 6; and from (1) and (3), that the terms are alternately positive and negative when the divisor...

...b" is divisible by a + b if n is odd, and by neither a + b nor a — b if n is even. (2) a" — bn is divisible by a — b if n is odd, and by both a...the quotient are all positive when the divisor is a — 6, and alternately positive and negative when the divisor is a + i; also, that the quotient is...

...4• &" is divisible by a + b if n is odd, and bij neither a + b nor a — b if n is even. 2. "" — b" is divisible by a — b if n is odd, and by both...alternately positive and negative when the divisor is a + 6 ; also, that the quotient is homogeneous, the exponent of a decreasing and of b increasing by 1...

...a" + b" is divisible by a + b if n is odd, and by neither a + b nor a - b if n is even. 2. a" — ba is divisible by a — b if n is odd, and by both a...the quotient are all positive when the divisor is a — 6, and alternately positive and negative when the divisor is а + 6 ; also, that the quotient is...