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If * is an operation 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

Solution:

To answer the given questions let us examine the problem deeply using the properties of integers and multiplication properties.

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

Now, substituting the values, a = (-3) and b = (-5) we get,

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

= 15 + (9 + 25)

= 15 + 34

= 49

ii.Now, a = -6 and b = 2

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

= -6 × 2 + (36 + 4)

= -12 + 40

= 28

✦ Try This: It is given that a * b = a × b + (a × a + b × b), then find the value of (-16) * 3

The above given question can be simplified using integer rules and by simply substituting a = -16 and b = 3 in the expression a * b = a × b + (a × a + b × b).

☛ Also Check: NCERT Solutions for Class 7 Maths Chapter 1

NCERT Exemplar Class 7 Maths Chapter 1 Exercise Problem 125

If * is an operation 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

Summary:

If * is an operation such that for integers a and b we have a * b = a × b + (a × a + b × b) then i. (-3) * (-5) = 49 ii. (-6) * 2 = 28

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