...difference of the squares of two numbers is equal to the product of their sum and difference. and. The square 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...

...of the sum of a,ny two quantities is deduced. THEOREM I. — The square of the sum of two quantities is equal to the square of the first, plus twice the product of the first by the second, plus the square of the second. EXAMPLES. 1. 2. 3. 4. 5. 0. 2oa;+4a2. Ans. Ans. Ans....

...difference of the squares of two numbers is equal to the product of their sum and difference. znd. The square 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...

...show some of its most simple applications. 78. Theorem I. — The square of the sum of two quantities is equal to the square of the first, plus twice the product of the first by the second, plus the square of the second. Let a represent one of the quantities, and ba +6 the...

...the parts separately hy the width ? Fig. 2. 25 feet. V 20 Ew* r 6 \JC b sir D F 20 20 20 5 400 100 the square of the sum of two numbers is equal to the squares of the numbers, pins twice their product. Thus, 25 being equal to 20-1-5, its square is equal...

...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...

...the squares of 20, 30, 40, 50, etc., are 400, 900, 1600, 2500, etc. Now since -(a+b)*=a'+2ab.+ b', the square of the sum of two numbers is equal to the...of the first, plus twice the product of the first by the second, plus the square of the second. Thus 212 = 20'+ 2(20+ 1) + 1 = 400+40+ 1 = 441. So 105*...

...reduce 53(a-6+c)-27(a+6-c)-26(a-6-c). 66. The three following theorems have very important applications. The square of the sum of two numbers is equal to the...of the first, plus 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?+ ab we obtain the...

...square, and then take the square root. By Theorem I., page 96, the square of the sum of two quantities is equal to the square of the first, plus twice the product of the first and second, plus the square of the second. Now here we may consider .7;3 the square of the first, and Qx...

...methods derived from the following theorems : Tfieorem I. 113. The square of the sum of two quantities is equal to the square of the first, plus twice the product of the first by the second, plus the square of the second, For, let a and 6 represent two quantities, then a + b...