Now we are going to learn how do you determine if a polynomial is the difference of two squares?
On looking at the polynomial we can simply identify if a polynomial is the difference of two squares or not, if we have the polynomial in the form of either ( a + b) * ( a – b )
Some times the Polynomials are big enough, but they do not look like the difference of two squares. We need to first write them as the perfect squares of the two Numbers.
It will be clearer with the following examples:
If the polynomial is (3x + y ) * ( 3x – y ), here we observed that the polynomial is similar to the identity a^2 – b^2 = ( a + b) * ( a – b )
So we can simply write it as (3x)^2 – ( y)^2, which will result to 9x^2 – y^2
In case we have a polynomial of the form 81y^4 - 16 x ^4
Here we will first write it as the perfect Square form and we will get :
= (9y^2) ^2 – (4x^2)^2
= (9y^2 – 4x^2) * ( 9y^2 + 4x^2)
= (3y)^2 – ( 2x)^2 * ( 9y^2 + 4x^2)
= (3y – 2x) *( 3y + 2x) * ( 9y^2 + 4x^2)
Thus by breaking of the terms of the polynomial in the form of the perfect square, help us to identify which identity will be applied.