What type of binomial will result in a difference of squares

If you have a binomial where both terms are a perfect square, you can factor it using difference of squares.

This also works when you have a number plus another number.

I'll provide two examples:

(x^2 - 9)

The difference of squares states: (a^2 - b^2) = (a + b)(a - b)

In this case, (x^2 - 9) = (x + 3)(x - 3)

We can also apply the difference of squares with a number plus another.

(x^2 + 25)

We can rewrite this binomial as: (x^2 - (-25))

Now, we can apply the same steps to factor.

(x^2 - (-25)) = (x + (√-25))(x - (√-25))

Because we have √-25, we can simplify it by multiplying it by i, which will remove the negative.

This leaves us with (x + 5i)(x - 5i), which is the factored form of x^2 + 25.

We can verify this by using FOIL.

x^2 - 5ix + 5ix - 25i^2

x^2 + 25i^2

i^2 can be interpreted as -1, and so we can change the + to -

x^2 - 25

the population of other specie of birds will decline or other specie of birds will find some alternate source of food to survive.

explanation:

according to the competitive exclusion principle, which is also known as gause's law, two specie living in the same niche and feeding on the same resource cannot co-exist stably.

as we have well studied the theory of natural selection which states that only those organisms survive which have better tendency to compete for food and adapt to the environmental conditions.

coming towards the question, what wi ll happen when one species outcompetes the other for the small fish , the other specie will not get enough food and will start to die or decline in population. eventually either other specie needs to find another alternative food source for itself or migrate at some other location where there is less competition otherwise it will just not exist anymore at that niche.

hope it !