...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...first by the second, plus the. square of the second. Thus, if we multiply a + b by a + b oa+ ab ab + b* we obtain the product a2 + 2ab + bz. of the result,...

...theorem? 4. What is a factor? 5. What is a co-efficient? 6. Prove that the square of the sum of any two quantities is equal to the square of the first...first by the second plus the square of the second. 7. Show that — 2a subtracted from 3a leaves 5a. 8. What signs of a fraction may be changed without...

...multiplication that are important on account of their frequent occurrence in algebraic operations. 85. I. The square of the sum of two quantities is equal to...first by the second, plus the square of the second. Thus, (x + y)2 = ж2 + 2xy + y2. (x + 3)2 = ж2 + 6ж + 9. 86. Write, by inspection, the squares of...

...This formula is the symbolical statement of the following rule : The square of the sum of two numbers is equal to the square of the first, plus twice the...first by the second, plus the square of the second. In the second case, (a -6)2 = a1-2ab + 62. (2) That is, the square of the difference of two numbers...

...(2) That is, the square of the difference of two numbers is equal to the square of the first, minus twice the product of the first by the second, plus the square of the second. In the third case, (a + b)(ab)=a2-b2. (3) That is, the product of the sum and difference of two numbers...

...expresses the Rule : — Tfte square of the difference of two quantities is the square of the first, minus twice the product of the first by the second, plus the square of ike second. Ex. 1. (x - 5)' =x' — lOx + 25. Ex. 2. (Зa - 2o)2 = (Зa)2 - 2 x Зa x 2b + (Щ' =•...

...right. Since the square of a number divided into any two parts is equal to the square of the first part, plus twice the product of the first by the second, plus the square of the second part (423), having found the square of the first part, which is 4900, the remainder 517 must be equal...

...right. Since the square of a number divided into any two parts is equal to the square of the first part, plus twice the product of the first by the second, plus the square of the second part (423), having found the square of the first part, which is 4900, the remainder 517 must be equal...

...II. — The square of the difference of two quart*titles is equal to the square of the first, minus twice the product of the first by the second, plus the square of the second. 1. (5-4)«=25— 40+16=1. 2. (2»— 6)2— 4a2— 3. (3*— 2yy= 4. (a2— y2)2=x*— 5. (ax— ar!)2=a...

...the terms of the dividend. 2. That the quotient is the square of the first term of the divisor, plus the product of the first by the second, plus the square of the second. Write two factors, one of which is the difference of the cube roots of the terms/ and the other the...