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Mathematical simplification of the first volume of junior one
+(c-a-b) square+square+square.

=a? -2ab+b? +b? -2ac+c? +c? -2ac+a?

=2a? +2b? +2c? -2ab-2bc-2ac

(2) Given a-b= 10 and b-c=5, use the conclusion in (1) to find the value of A +b +c -ab-bc-ca.

∫a-b = 10 b-c = 5

∴a-c= 15

Square of a+square of b+square of c-ab-BC-ca.

=(2a? +2b? +2c? -2ab-2bc-2ac)÷2

=[(a-b)? +(b-c)? +(A-C)? ]÷2

=( 10? +5? + 15? )÷2

=( 100+25+225)÷2

=350÷2

= 175