Laws of Algebra

Using the Commutative Law for Addition stated above

`a + b = b + a`

=> For the given expression, x = 5

Using of the Commutative Law For Multiplication stated above

=> For the given expression, r = 2

According to the Distributive Law, we have

Through comparison of the given expression with the above formula, we conclude that

We can also prove that m = 2 by method of equating the two sides of the given expression as shown below.

Given that

L.H.S (Left Hand Side) = 2 . ( 3 + 1 )

R.H.S (Right Hand Side) = ( 2 . 3 ) + ( m . 1 )

By equating the two sides,

Hence we get the same answer as we got using the Distributive Formula.

Here we make use of the Associative Law For Multiplication which states that for any variables a, b and c

Through comparison we get

Using the Cancellation law For Addition

Here a = x, b = 5, c = 2

And the formula states that the identity will hold if and only if a = b i.e., if x = 5

Using the Cancellation law For Multiplication

Here

a = n

b = 5

c = 3 != 0

Hence the equation will hold if and only if a = b, that is if n = 5

We have studied Distributive law which states that

`a . ( b + c ) = ( a . b ) + ( a . c )`

Here we can split up 14 = 10 + 4

Hence we can split our problem using this property and find the solution with greater ease.

We have studied that in the distributive property, we distribute the operation of multiplication over addition. We can use this property to simplify the above expression.

We see that both 3, and 9 are multiples of 3. So if we take 3 out of the above expression, leaving the rest inside the parentheses, what we get is a distributed equivalent of the above expression.

A mentionable point here is that the property also holds for subtraction. For example

Using the Associative Property for Multiplication