Question

If  ‘*’ is an operation have, such that for integers a and b. We have  a * b = a × b+(a × a + b × b), then find

(i) (-3)*(-5)

(ii) (-6)*2

Answer 1

(i) We have, a * b = a × b +(a × a + b × b)

Now, put a = (-3) and b = (-5)

(-3)* (-5) = (- 3) × (- 5)+ [(- 3) × (- 3)+ (- 5) × (- 5)]

= 15 + (9 + 25)= 15 + 34 = 49

(ii) Now, put a = – 6 and b = 2

(-6)*2 = (-6) × 2 +[(-6) × (-6) + 2 × 2

= -6 × 2 + (36 + 4)= -12 + 40= 28