Question

How do you simplify $\left( {x - 5} \right)\left( {x + 5} \right)$ ?

Answer 1

Hint: Here they have asked to simplify the expression $\left( {x - 5} \right)\left( {x + 5} \right)$. Expand the given expression using FOIL method, where FOIL stands for first, outer, inner, last. After expanding, simplify the expression to get the required answer.

Complete step by step answer:
In this question they have asked to simplify the given expression which is $\left( {x - 5} \right)\left( {x + 5} \right)$. Expand the given expression using the FOIL method, FOIL stands for first, outer, inner, last. The formula for expansion using the FOIL method is given by: $(a + b)(c + d) = ac + ad + bc + bd$.
Now, apply distributive property for the given expression $\left( {x - 5} \right)\left( {x + 5} \right)$ , we get
$ \Rightarrow x(x + 5) - 5(x + 5)$
In order to simplify the above expression, we can again apply the distributive property. Therefore we get
$ \Rightarrow x.x + x.5 - 5.x - 5.5$
Now, perform multiplication operation as in the above expression to simplify further, we get
$ \Rightarrow {x^2} + 5x - 5x - 25$
As we can see in the above expression we have $ + 5x$ and $ - 5x$ which will become zero or which gets canceled. So now, the above expression can be written as
$ \Rightarrow {x^2} + 0 - 25$
Hence we can write as ${x^2} - 25$.

Therefore the simplified form of $\left( {x - 5} \right)\left( {x + 5} \right)$ is ${x^2} - 25$, which is an example for the DOTS method. DOTS is nothing but the difference of two square methods.

Note:
Whenever we have this type of problem on simplification, we can make use of the foil method formula directly to expand and simplify the expression to get the required answer or we can apply the distributive property to expand the expression and simplify further. Both methods are similar. Whichever method you are familiar with, you can make use of the same and get the correct answer.