In this video, you will learn how to prove
a mathematical expression whether it is divisible
by a constant or not
We say a mathematical expression is divisible
by a constant k if it can be factorised into
two brackets, in which one of them is the
multiple of k.
The expression we are using here is 7^(x+2)+7^x-154(7^(x-1))
We want to prove that it is divisible by 7
by factorising it into two brackets in which
one of the brackets is the multiple of 7
Let's start to prove it
First, separate all the indices using the
law of indices.
7^(x+2) can be written as 7^x multiply 7^2
while 7^(x-1) can be written as 7^x over 7
Then, simplify the expression.
You can see that all the three terms have
7^x
So, factorise the term 7^x.
The first term left with 49, plus the second
term 1, minus the third term 22
Finally, you obtain 28 multiply 7^x
Since 28 is the multiple of 7, therefore the
expression 7^(x+2)+7^x-154(7^(x-1)) is divisible
by 7
