[ Home ] [ FOIL Method ] [ Double & Half Method ] [ Squaring Numbers ] [ Squaring Num End In 5 ] [ Squaring Num End In 6 ] [ Squaring Num End In 7 ] [ Squaring Num End In 8 ] [ Squaring Num End in 9 ] [ Squaring Nums 40-49 ] [ Squaring Nums 50-59 ] [ Squaring Nums 90-99 ] [ Difference of 2 Squares ] [ Mult Nums End in 5 ] [ Mult Nums One's Add 10 ] [ Mult Nums One's Add 5 ] [ Mult Nums Same Ten's Digits ] [ Mult Nums Tens Add 10 ] [ Mult Nums Less 100 ] [ Mult Nums More 100 ] [ Mult Nums More 100 Less 100 ] [ AB + BC ] [ AA + 2AA ] [ AA + 3AA ] [ AA + 7AA ] [ AA + 10AA ] [ Mult Nums Less 1000 ] [ Mult Nums More 1000 ] [ Add 2 Squares ] [ Product of 4 Nums ] [ Adding Consecutive Squares ] [ Squaring: 101a ] [ Adding Squares #2 ]

(*View/Download .pdf file)

(***) Adding Squared Numbers In The Form:  (10a + b)² + [10(b-1) + (10-a)]²:

   A.  This method is simple once we reduce this form:

(10a + b)² + [10(b-1) + (10-a)]² = 101(a² + b²)

   B.  Using numbers instead of variables we get the following:

1.      Square the one’s digit on the left number.

2.      Square the ten’s digit on the left number.

3.      Add the result of step 1 and step 2.

4.      Multiply the result of step 3 by 101 for the answer.  See Multiplying by 101.

   C.  This method is sometimes hard to recognize.  If the inside numbers subtract to 1 and the outside numbers add to 10 then you can use this method.

Ex [1]  43² + 26² =_________.

a)  3² + 4² = 9 + 16 = 25.

b)  25 x 101 = 2525.

c)  The answer is 2525.

Ex [2]  65² + 57² =_________.

a)      If you look at this equation it does not fit the pattern.  But if you switch the two numbers it does.  So think of this as being 57² + 65².

b)      5² + 7² = 25 + 49 = 74.

c)      74 x 101 = 7474.

d)      The answer is 7474.

Back to top