"Explain how you can recognize a special product of binomials. Give examples of each type."
(please help i need this done soon :(, thank you)

See below.

Step-by-step explanation:

1. Difference of 2 squares.

For example x^2 - 4

We recognise this by the fact that x^2 and 4 are perfect squares separated by the negative sign,  and the factors are (x + 2) and (x - 2).

In general form this is  a^2 - b^2 = (a - b)(a + b).

2. Perfect square trinomial.

This is the product of 2 identical binomials.

For example:

(x + 2)(x + 2) = x^2 + 4x + 4.

We recognise this  by the last and 2 terms are perfect squares and the term in x has a coefficient which is 2 times the square root of the last term.

In the above  the 4  (in the 4x) = 2*√4.

let's add {f(x)=x+1}f(x)=x+1 and {g(x)=2x}g(x)=2x together to make a new function.

f(x)+g(x) =(x+1)+(2x)=x+1+2x=3x+1

let's call this new function hh. so we have:

{h(x)}={f(x)}+{g(x)}{=3x+1}h(x)=f(x)+g(x)=3x+1

we can also evaluate combined functions for particular inputs. let's evaluate function hh above for x=2x=2. below are two ways of doing this.

method 1: substitute x=2x=2 into the combined function hh.

h(x)

h(2)

​    

=3x+1

=3(2)+1

=7

​ since h(x)=f(x)+g(x)h(x)=f(x)+g(x), we can also find h(2)h(2) by finding f(2) +g(2)f(2)+g(2).

first, let's find f(2)f(2):

f(x)

f(2)

​    

=x+1

=2+1

=3

​  

now, let's find g(2)g(2):

g(x)

g(2)

​    

=2x

=2⋅2

=4

​  

so f(2)+g(2)=3+4=\greend7f(2)+g(2)=3+4=7.

notice that substituting x =2x=2 directly into function hh and finding f(2) + g(2)f(2)+g(2) gave us the same answer!