Question 125 (i)

If '' is an operation have, such that for integers a and b. We have
$a b = a \times b + (a \times a + b \times b),$ then find
$(- 3) * (- 5)$

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Solution

We have, $a * b = a \times b + (a \times a + b \times b)$
Now, put a = (-3) and b = (-5)
$(- 3) * (- 5) = (- 3) \times (- 5) + [(- 3) \times (- 3) + (- 5) \times (- 5)] = 15 + (9 + 25) = 15 + 34 = 49$

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Question 126 (i)

If $Δ$ is an operation, such that for integers a and b. We have $a Δ b = a \times b - 2 \times a \times b + b \times b (- a) \times b + b \times b,$ then find
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Also, show that $4 Δ (- 3) \neq (- 3) Δ 4$

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Distributive Property

Standard IX Mathematics

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Question 125 (i) If '*' is an operation have, such that for integers a and b. We have a∗b=a×b+(a×a+b×b), then find (−3)∗(−5)

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

Question 125 (i)

If '' is an operation have, such that for integers a and b. We have
$a b = a \times b + (a \times a + b \times b),$ then find
$(- 3) * (- 5)$

We have, $a * b = a \times b + (a \times a + b \times b)$
Now, put a = (-3) and b = (-5)
$(- 3) * (- 5) = (- 3) \times (- 5) + [(- 3) \times (- 3) + (- 5) \times (- 5)] = 15 + (9 + 25) = 15 + 34 = 49$