...4. (5a 2 +2&) 2 ^ 9. 5. (5a*+b) 2 = 10. 67. The square of the difference of two numbers is equal to the square of the first, minus twice the product of...first by the second, plus the square of the second. Thus, if we multiply a— b by a—b a 2 — ab - ab+b* we obtain the product a 2 —2ab+b 2 . EXAMPLES....

...¿) (a— i) = a'— ïab+V Or, in words, The square of the difference of two quantities is equal to the square of the first, minus twice the product of the first and second, phis the square of the second. III. (a+l) (a_b)=a«_ £,' Or, in words, The product of...

...two quantities is deduced. THEOREM II. — The square of the difference of two quantities is equal to the square of the first, minus twice the product of...first by the second, plus the square of the second. EXAMPLES. 1. 2. 3. 4. 5. **. 'J — ~4f — "g Y~TTn — r44 x — y)2=(x — y] (xy)=x2 — 2xy-\-y-....

...(2m+3n)2=4m2-f I2wm+9n2. 79. Theorem II. — The square of the difference of two quantities is equal to the square of the first, minus twice the product of...first by the second, plus the square of the second. Let a represent one of the quantities, and 6 a — 6 the other. a — b Then, a — 6= their difference;...

...(a — 5) = a2 — 2a6 + 52. (2) That is, The square of the difference of two quantities is equal to the square of the first, minus twice the product of...first by the second, plus the square of the second. Also, (a _|- 5) (a — 5) = a2 — 52. (3) That is, jTAe product of the sum and difference of two quantities...

...360+ 9= 3969, etc. Again, since (a— by=a' — 2«5-t-6", the square of the difference of two numbers equals the square of the first, minus twice the product...first by the second, plus the square of the second. Thus 19" = 400—40+2 = 361. 95" = 10000—1000+25 = 9025. 85'= 8100— 900+25 = 7225. 57"= 3600- 360+...

...+ a*? Ans. 9+6ai + at. Theorem, II. 114. The square of the difference of two quantities is equal to the square of the first, minus twice the product of...first by the second, plus the square of the second. • For, let a and b represent the two quantities, then a — b will denote their difference, and (ab)s...

...(5a+36)2= 8. 4. (5a2+ 26)2= 9. 5. 5a3+i= 10. 67. T/ie square of the difference of two numbers is equal to the square of the first, minus twice the product of the first by the sec~ and, plus the square of the second. Thus, if we multiply a— 6 by a— b a?— ab - ab+bz we...

...ab + V states. as + 2 ab + b2 Theorem II. The square of the difference of two quantities is equal to the square of the first, minus twice the product of the first and second, plus the square of the second. a — b PROOF. Let a and b stand for any a — b two quantities....

...is a quantity consisting of two terms, and its square is equal to the square of the first term, plus twice the product of the first by the second, plus the square of the second. Let 35 be written 30 + 5. Then, squaring this number, by multiplying each part separately, we hare,...