Q125 of 147 Page 8

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

We have been given that,

a * b = a × b + (a × a + b × b) …(i)


Apply the same formula in the questions that follows:


(i). We have (-3) * (-5).


Put a = -3 and b = -5 in equation (i), we get


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


⇒ (-3) * (-5) = 15 + (9 + 25)


⇒ (-3) * (-5) = 15 + 9 + 25


⇒ (-3) * (-5) = 49


Thus, the answer is 49.


(ii). We have (-6) * 2.


Put a = -6 and b = 2 in equation (i), we get


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


⇒ (-6) * 2 = -12 + (36 + 4)


⇒ (-6) * 2 = -12 + 40


⇒ (-6) * 2 = 28


Thus, the answer is 28.


More from this chapter

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123

You are at an elevation 380 m above sea level as you start a motor ride. During the ride, your elevation changes by the following metres: 540 m, –268 m, 116 m, –152 m, 490 m, –844 m, 94 m. What is your elevation relative to the sea level at the end of the ride?

 124

Evaluate the following, using distributive property.

(i) –39 × 99


(ii) (– 85) × 43 + 43 × (– 15)


(iii) 53 × (– 9) – (– 109) × 53


(iv) 68 × (–17) + ( –68) × 3

 126

If ∆ is an operation such that for integers a and b we have

a ∆ b = a × b – 2 × a × b + b × b (–a) × b + b × b


then find (i) 4 (– 3)


(ii) (– 7) ∆ (– 1)


Also show that 4 ∆ (– 3) ≠ (– 3) ∆ 4


and (– 7) ∆ (– 1) ≠ ( – 1) ∆ (– 7)

 127

Below u, v, w and x represent different integers, where u = –4 and x ≠ 1. By using following equations, find each of the values:

u × v = u


x × w = w


u + x = w


(a) v


(b) w


(c) x


Explain your reasoning using the properties of integers.