...a — b 1 fe — 6 a — b a2 — 06 . . ' _ a 6 4. 62 n« *- 2 ab + 6s. That is, <Ae second power of the difference of two quantities is equal to the sum of their second powers, diminished by twice their product. . , 20. An artist sold to A and B two pictures...

...adding them together : thus, and 36aV + 60a3^3 + 25aix3 = (Sax2 + 5aV)2, or x X (6ax2 + 5aV). . 2. The square of the difference of two quantities is equal to the sum of their squares, minus twice their product. Let a be the greater of two quantities, and b the lesSi then...

...thus, X (8a25 + 10a6), and 36a2^ + 60a3#3 + 25a4#2 = (6a#2 + 5a2#)2, or 2-) x (6a#2 + 5as#). 2. 7Vte square of the difference of two quantities is equal to the sum of their squares, minus twice their product. Let a be the greater of two quantities, and b the less, then...

...twice the product of the first and second. 2°. That (o — b) (a — i) = a* — 2o6 + V ; or, that the square of the difference of two quantities is equal to the square of the first, plug the square of the second, minus twice the product of the first and second....

...is equal to the sum of their squares, plus twice their product." From the 3rd of these we see that "The square of the difference of two quantities, is equal to the sum of their squares, minus twice their product." Multiply 2x+b Multiply bx*— 2x by 3x-7 by 6x*+7x 6жа+15ж...

...second. 17. Multiply a — b by a — b. The product is a2 — 2a6+62 ; from which we perceive, that 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....

...most common mistakes of beginners is to call the square of а + b equal to a2 + 62. THEOREM II. (61.) 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....

...most common mistakes of beginners is to call the square of o + b equal to a2 + 62. THEOREM II. (61.) 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....

...(2+5)2=4+20+25=49. ALGEBRAIC THEOREMS. 3 . (oa+iy) 2=aV+2 abxy+tfy*. 4. (ax2+3;i:z3)2 ART. 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....

...a— 6 a2 — a6 — ab+V But a—b is the difference of tho quantities a and b ; hence 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 tecond, plus the sqitare of the second....