Question

$\left[\right(-8)\times (-3\left)\right]\times (-4)$ is not equal to

• A. $(-8)\times \left[\right(-3)\times (-4\left)\right]$
• B. $\left[\right(-8)\times (-4\left)\right]\times (-3)$
• C. $\left[\right(-3)\times (-8\left)\right]\times (-4)$
• D. $\left[\right(-8)\times (-3\left)\right]-\left[\right(-8)\times (-4\left)\right]$

Answer 1

The correct option is D

$\left[\right(-8)\times (-3\left)\right]-\left[\right(-8)\times (-4\left)\right]$

The given expression is in the form of the $associativepropertyofaddition.$

The multiplication follows associative property i.e. regardless of how numbers are parenthesized the final product of the numbers will be the same.

The $associativeproperty$of $addition$and $multiplication$states that the way a grouping of numbers doesn’t matter; the result will be the same. One can group numbers in any way but the answer will remain the same. Parenthesis can be done, irrespective of the order of terms. Let $x,y,andz$ be any three integers, then

i) $x+(y+z)=(x+y)+z$

ii ) $x\times (y\times z)=(x\times y)\times z$

above is showing the $associativeproperty$

According to the given question, using the below property

$x\times (y\times z)=(x\times y)\times z$

$x=-8$ $y=-3$ $z=-4$

By using $associativeproperty$

$(-8)\times \left[\right(-3)\times (-4\left)\right]$$=$$\left[\right(-8)\times (-4\left)\right]\times (-3)$ $=$$\left[\right(-3)\times (-8\left)\right]\times (-4)$ are following $associativeproperty$of $multiplication$

$\left[\right(-8)\times (-3\left)\right]-\left[\right(-8)\times (-4\left)\right]$is not following $associativeproperty$of $multiplication$

So, $\left[\right(-8)\times (-3\left)\right]-\left[\right(-8)\times (-4\left)\right]$is the correct option

Hence, $\left[\right(-8)\times (-3\left)\right]\times (-4)$ is not equal to $\left[\right(-8)\times (-3\left)\right]-\left[\right(-8)\times (-4\left)\right]$

So, option $(D)$is the correct option.