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Integers — MATHS STD 7 — Question

Gujarat BoardEnglish MediumSTD 7MATHSIntegers3 Marks
Question
If $\triangle$ is an operation such that for integers a and b we have $ a \triangle b$
$= a \times b -2 \times a \times b + b \times b (-a) \times b + b \times b$ then find.
$4\triangle(-3)$
✓

Answer

We have, $\text{a}\ \triangle\ \text{b}$
$= a \times b - 2 \times a \times b + b \times (b) \times (-a) b + b \times b$
Now, put $a = 4$ and $b = (-3)$
$4 \triangle (-3) = 4 \times (-3) - 2 \times 4 (-3) + (-3) \times (-3)(-4) \times (-3) + (-3)\times (-3)$
$= -12 - 2 \times (-12) + (9) \times (12) + 9$
$= -12 + 24 + 108 + 9 = 129.$
Now, put $a = -3$ and $b = 4$
$\Rightarrow (-3) \triangle 4 = (-3) 4 - 2 \times (-3) \times (-4) + 4 \times 4\{-(-3)\} \times 4 + 4 \times 4$
$= (-12) + 24 + 16(3) \times 4 + 16$
$= (-12) + 24 + 192 + 16$
$= 220$
Clearly, $4\triangle(-3)\neq(-3)\triangle4$
 

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