...= 4 я? + 20 xy + 25 y\ 3. By actual multiplication, we have That is, the square of the difference of two numbers is equal to the square of the first number, minus twice the product of the two numbers, plus the square of the second number. 4. Observe that this...

...square of (a — &) differ from the square of (а+&)? 93. PRINCIPLE. — The square of the difference of two numbers is equal to the square of the first number, minus twice the product of the first and second, plus the square of the second. EXAMPLES Expand by...

...multiplication, we have (a - e)1 = (a - 6) (a - 6)= as - 2a6 + b\ That is, the square of the difference of two numbers is equal to the square of the first number, minus twice the product of the two numbers, plus the square of the second number. Eg, (3 x - 7 y)*...

...The first example gives the value of (a -)- b) (a -f- b), that is, of (aj-6)8; we thus find Hence, the, square of the sum of two numbers is equal to the sum of the squares of the two numbers phis twice the product of the first times the second. Again we...

...The first example gives the value of (a -\- b) (a -f- b), that is, of (af b)"; we thus find Hence, the square of the sum of two numbers is equal to the sum of the squares of the two numbers plus twice the product of the ßrst_ times the second. Again...

...use the exponent to save + ab + b3 repetition. From the work, the following principle is derived: — The square of the sum of two numbers is equal to the square of the first, plus two times the first by the second, plus the square of the second. 2. Multiply а - b by a ~b,...

...the sum of two numbers obtained from the numbers? 3. What signs have the terms ? 91. PRINCIPLE. — The square, of the sum of two numbers is equal to the square of the ßrst number, plus twice the, product of the Jirxt and second, plux the minare of the second. Since...

...Multiplying by 20 202 + 20 x 5 Multiplying by 5 20 x 5 + 52 202 + 2(20 x 5) + 52 = 400 + 200 + 25 = 625. 414. The square of the sum of two numbers is equal to the square of the first + twice the product of the first by the second + the square of the second. 132=(10 + 3)2= 102 + 2(10x3)+32=?...

...the sum of two numbers. By multiplication, we have (x +/)2 = O +/) O +/) = x' + 2 xy +/-. That is, the square of the sum of two numbers is equal to the square of the first, plus twice their product, plus the square of the second. Thus, and = 42+2(4x3) + 32 = 49; x26) +462,...

...Involution. In squaring and cubing numbers the following Algebraic principles are very useful : — (1) The square of the sum of two numbers is equal to the sum of the squares of the numbers 4- twice the product. (2) The square of the difference of two numbers...