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### Grade 7 - Mathematics4.10 Identities - I

 An equation which is true for all real values of its variables is called an identity.  This is denoted by the symbol "º" Example: Show that the equation (a-b)2 = a2 - 2ab + b2 is an identity. Solution: Substituting a = 2 and b =1 in the equation, LHS = (2-1)2 = 12 = 1 RHS = 22 - 2.2.1 + 12 = 4 - 4 + 1 = 1 LHS = RHS.  Hence equation is true for values 2 and 1. Similarly it can be proved that the equation becomes a true statements for any pair of real numbers Direction: Show that the following equations are in identities or not, taking any pair of real numbers and prove.
 Q 1: (a-b)2 = a2 - 2ab + b2, is this statement is true for any pair of real numbers?FalseTrue Q 2: x2-9 = (x-3)(x-3), is this statement is true for any pair of real numbers?FalseTrue Q 3: (x-y)(x+y) = x2 - y2, is this statement is true for any pair of real numbers?TrueFalse Q 4: a(a+b) = ab + ac, is this statement is true for any pair of real numbers?FalseTrue Q 5: (a+b)(c+d) = ac + ad + bc + bd, is this statement is true for any pair of real numbers?FalseTrue Q 6: 2(x+4y) = 2(2x+4y), is this statement is true for any pair of real numbers?TrueFalse Question 7: This question is available to subscribers only! Question 8: This question is available to subscribers only!

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