1.3.6 Difference of Squares

Everybody should know that x2y2=(xy)(x+y)x^2 - y^2 = (x - y)(x + y). You can easily apply this trick when asked to find the difference between squares of numbers. For example:

542552=(5455)(54+55)=10954^2 - 55^2 = (54 - 55)(54 + 55) = -109

This is a pretty basic trick and is easily recognizable on the test.

Problem Set 1.3.6

Here are some more practice to give you a better feel of the problems:

73² - 72²
36² - 34²
57² - 58²
67² - 66²
69² - 67²
54² - 55²
67² - 65²
88² - 87²
48² - 49²
97² - 96²
77² - 76²
54² - 53²
42² - 44²
4.7² - 3.3²
1.3² - 2.6²
65² - 64² + 63² - 62²
24² - 6²
56² - 55² + 54² - 53²
76² - 74²
3.5² - 6.5²
22² - 23² + 24² - 25²
55² - 50²
83² - 82² + 81² - 80²
55² - 52²
44² - 43² + 42² - 41²
111² - 110² + 109² - 108²
11² - 22²
77² - 76² + 75² - 74²
63² - 57²
56² - 55² + 54² - 53²
59² - 71²
16² - 17² + 18² - 19²
41² - 42² + 43² - 44²
18² - 6²
x² + 16² = 19², x² =
4.5² - 1.5²
21² - 20² + 19² - 18²
58² - 59² + 60² - 61²
72² - 78²
24² - 22² + 20² - 18²
89² - 86² + 83² - 80²
48² - 62²
74² - 76² + 78² - 80²
38² - 27²
31² - 33² + 35² - 37²
48² - 44² + 40² - 36²
79² - 76² + 73² - 70²