Question

State the property :- ax(bxc)= axb + axc​

Answer 1

Step-by-step explanation:

I believe your Question was,

"State the property:- a(b + c) = ab + ac"

It is called Distributive Property

It is an important result for arithmetics and especially algebra

We can prove this as well,

LHS = a × (b + c) or a(b + c)

RHS = ab + ac

We know that,

mn + mp = m(n + p)

because m is a common factor

Similarly,

RHS = ab + ac

Here a is common so we can factor it out,

= a(b + c) = LHS

Thus,

LHS = RHS

We can also prove it geometrically as well,

(Refer the above image....)

Let us take two rectangles of length 'a' units (for both) and breadth 'b' and 'c' units respectively,

Now, arrange them along the breadth such that it forms a new rectangle of length 'a' units and breadth '(b + c)' units

Now, the area of the new rectangle must be equal to the area of the initial two rectangles (Think about it.......)

We know that, Area = length × breadth

Thus,

Area of 1st rectangle = a × b = ab

Area of 2nd rectangle = a × c = ac

Area of the new rectangle = a × (b + c) = a(b + c)

And accordingly we said the sum of areas of the 2 rectangles must be equal to the new rectangle formed

Hence,

a(b + c) = ab + ac

Thus, proved.

Hope it helped and you understood it........All the best