...b) = a2 - b\ a'- 6' , , a'— &' ,1 -a .'. — = a — b, ana — = a + b. Hence a+b a—b RULE 1. The difference of the squares of two numbers is divisible by the sum, and by the difference, of the numbers. Exercise 24. Write by inspection the quotient of a' -4 14. x—(y+z)...

...Squares. From § 81, (a + 6)(a - ¿) = a2 - 62. =ab, and ^-^ = ci + 6. Hence, a + ba — b RULE 1. The difference of the squares of two numbers is divisible by the sum, and by the difference, of the numbers. Exercise 24. Write the quotient of 1-4ж2 9 49 -4a2 1-2z' "7-2a''...

...V. as-¿2 , , a2— V . , TT /. - r = a — 6, and - - r- = a + 6. Hence a+oa — о RULE 1. ТЛe difference of the squares of two numbers is divisible by the sum, and by the difference, of the numbers. Exercise 24. Write by inspection the quotient of 1. 2. 3. 4. 5....

...difference between the nth powers of a of and Note. The difference of the squares of two numbers is always divisible by the sum and also by the difference of the numbers. Thus, аб — 48 ¡s divisible by i/8 ^ ¿4. In general, a2» — 62m is divisible by an ¿ bm when...

...Squares. Since (c»rf- 6)(a - 6) = a' - b\ .: -2lzi|! = a_6; and 2-=l|!=a + 6. Hence a + oa — o RULE 1. The difference of the squares of two numbers is divisible by the sum, and by the difference, of the numbers. Exercise 28. Write by inspection the quotient of : 1. з? — 4...

...between the w.th powers of axp and by'*. Note. The difference of the squares of two numbers is always divisible by the sum and also by the difference of the numbers. Thus, a' — 68 is divisible by o8 ib*. In general, a2" — б2"1 is divisible by a" ± 6™ when n...

...Squares. a2-62 , a2 -62 , , ,, - — — = а — £г; - — = a + b. Hence. a + ba — b RULE 1. The difference of the squares of two numbers is divisible by the sum of the numbers, and the quotient is the difference of the numbers. The difference of the squares of...

...„2 _ 7.2 Œ — О ? » — О . _T - — - = a — b ; - - = a + b. Hence, a + ba — b RULE 1. The difference of the squares of two numbers is divisible by the sum of the numbers, and the quotient is the difference of the numbers. The difference of the squares of...

...Numbers. 1. By actual division, we have (а2-А2)ч-(а + 6)=а-6 and (a" - 6s) ч- (а - Ь) = а + b. That is, the difference of the squares of two numbers is exactly divisible by Ifie sum oflhe numbers, and also by th? difference of the numbers, taken in the...

...numbers is divisible by the sum of the numbers, and the quotient is the difference of the numbers. The difference of the squares of two numbers is divisible by the difference of the numbers, and the quotient is the sum of the numbers. EXERCISE 33. Write by inspection...