...tJte siim, of the squares of the two numbers increased by twice their product. • Again we have Thus the square of the difference of two numbers is equal to the sum of the squares of the two numbers diminished by twice their product. Abo we have (a + b)(ab) =...

...EXAMPLES. 1. (3a+bf^ 6. 2. (Sa+3b)*= 7. 3. (5a+3Z>) 2 = 8. 4. (5a 2 +2&) 2 ^ 9. 5. (5a*+b) 2 = 10. 67. The square of the difference of two numbers is equal...of the first, minus twice the product of the first by the second, plus the square of the second. Thus, if we multiply a— b by a—b a 2 — ab - ab+b*...

...l)'=(a— ¿) (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 the sum and...

...4 a:2 +12 xy -\- 9 #2. AQ r» _J_ A THEOREM III. 59. The square of the difference of two quantities is equal to the square of the first, minus twice the product of the two, plus the square of the second. Let a and b represent the two quantities, and a ^> 6 ; their difference...

...twice the rectangle contained by the whole and that part together with the square of the other part. 4. The square of the difference of two numbers is equal to the sum of the squares of the two numbers diminished by twice their product. Prove this both geometrically...

...of the sum of two numbers is equal to the sum of the squares together with twice the product. 3rd. The square of the difference of two numbers is equal to the sum of the squares less twice their product. If we take the numbers as measures of lines, these facts...

...difference of any 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 the first by the second, plus the square of the second. EXAMPLES. 1. 2. 3. 4. 5. **. 'J — ~4f — "g Y~TTn...

...of the sum of two numbers is equal to the sum of the squares together with twice the product. 3rd. The square of the difference of two numbers is equal to the sum of the squares less twice their product. If we take the numbers as measures of lines, these facts...

...(2+5)2=4+20+25=49. 2. (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 the first by the second, plus the square of the second. Let a represent one of the quantities, and 6 a — 6...

...(a — 5) (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 the first by the second, plus the square of the second. Also, (a _|- 5) (a — 5) = a2 — 52. (3) That is, jTAe...