A binary operation * is defined on the set \(T = \{-2,-1,1,2\}\) by \(p*q = p^2 + 2pq - q^2\), where \(p,q \in T\). Copy and complete the table. * -2 -1 1 2...

Answer Details

p*q = p2 ${}^2$ + 2pq - q2 ${}^2$

when p = -2 and q = -2

p*q = -22 ${}^2$ + 2(-2)(-2) - (-2)2 ${}^2$
p*q = 4 + 8 - 4 = 8

when p = -2 and q = -1
p*q = -22 ${}^2$ + 2(-2)(-1) - (-1)2 ${}^2$
p*q = 4 + 4 - 1 = 7

when p = -2 and q = 1
p*q = -22 ${}^2$ + 2(-2)(1) - (1)2 ${}^2$
p*q = 4 - 4 -1 = -1

when p = -1 and q = -2
p*q = -12 ${}^2$ + 2(-1)(-2) - (-2)2 ${}^2$
p*q = 1 + 4 - 4 = 1

when p = -1 and q = -1
p*q = -12 ${}^2$ + 2(-1)(-1) - (-1)2 ${}^2$
p*q = 1 + 2 -1 = 2

when p = -1 and q = 2
p*q = -12 ${}^2$ + 2(-1)(2) - (2)2 ${}^2$
p*q = 1 - 4 - 4 = -7

when p = 1 and q = -2
p*q = 12 ${}^2$ + 2(1)(-2) - (-2)2 ${}^2$
p*q = 1 - 4 - 4 = -7

when p = 1 and q = -1
p*q = 12 ${}^2$ + 2(1)(-1) - (-1)2 ${}^2$
p*q = 1 - 2 - 1 = -2

when p = 1 and q = 1
p*q = 12 ${}^2$ + 2(1)(1) - (1)2 ${}^2$
p*q = 1 + 2 - 1 = 2

when p = 1 and q = 2
p*q = 12 ${}^2$ + 2(1)(2) - (2)2 ${}^2$
p*q = 1 + 4 - 4 = 1

when p = 2 and q = -2
p*q = 22 ${}^2$ + 2(2)(-2) - (-2)2 ${}^2$
p*q = 4 - 8 - 4 = -8

when p = 2 and q = -1
p*q = 22 ${}^2$ + 2(2)(-1) - (-1)2 ${}^2$
p*q = 4 - 4 - 1 = -1

when p = 2 and q = 1
p*q = 22 ${}^2$ + 2(2)(1) - (1)2 ${}^2$
p*q = 4 + 4 - 1 = 7
when p = 2 and q = 2
p*q = 22 ${}^2$ + 2(2)(2) - (2)2 ${}^2$
p*q = 4 + 8 - 4 = 8