...x" -j- 3 y and difference 5 x2 — 3y. 6. Sum 2 a — 8b and difference 10 a + 1* b. THEOREM II. 58. The square of the sum of two quantities is equal to...square of the first, plus twice the product of the two, plus the square of the second. Let a and 6 represent the two quantities ; their sum will be a...

...difference 5 x2 — 3 y. 6. Sum 2 a — 8 b and difference 10 a + 14 5. THEOREM II. 58. The square of (he sum of two quantities is equal to the square of the first, plus twice the product of the two, plus the square of the second. Let a and 6 represent the two quantities ; their sum will be a...

...The three following theorems have very important applications. The square of the sum of two numbers is equal to the square of the first, plus twice the product of the first ly the second, plus the square jof the second. Thus, if we multiply a+6 by a+6 a 2 + ab ab+b* we. obtain...

...following theorems give rise to formulas, useful in abridging algebraic operations. THEOREM I. 76. The square of the sum of two quantities is equal to the square of the firsl, plus twice the product of the first by the second, plus the square of the second. For, let a...

...b) = a- — 2a¿ + Ir ; and (а + Ъ)(а — Ь) =á* — b'-. From this example it appears that 1. The square of the sum of two quantities is equal to the и«.'» of their squares, together with twice their product. 2. The square of the difference of two...

...the indicated operations, the resulte which follow: Or, expressing the result in words, The »guare of the sum of two quantities is equal to the square of the first, plus twice the product of the ßrst and second, plus the square of the second. II. (a— 6)'=(o— b) (a— 6)=a'— 2ab+b' Or, in...

...eachJ^^azs^A has $50,000, and B has $70,000. SECTION XXV. Factoring. Fundamental Theorems. Theorem L The square of the sum of two quantities is equal to...of the first, plus 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 -J- b two quantities....

...partial products as they stand, even without first adding the products by a and ft. QBD 85. THEO. — The square of the sum of two quantities is equal to...square of the first, plus twice the product of the two, plus the square of the second. 86. THEO. — The square of the difference of two quantities is...

...and b represent any two quantities whatever, then, (a + ¿)2 = (a + ¿) (a -fb) = a2 + 2ab + ¿2. (1) That is, The square of the sum of two quantities is equal to the square nf tlie first, plus twice the product of the first by the second, plus the square of the second. Again,...

...4. 24. Multiply (а + и)2 by (а - о)3. Ans. а5 — а4о — 2asô2 + 2asô3 + ai4 — б5. 71. The square of the sum of two quantities is equal to the sum of their squares increased by twice their product. If we multiply a + Ъ by a + b %e obtain a2...