The answer is:
The third option,
[tex]x^{2}+mx+m=(x+2)^{2}[/tex]
We are looking for an equation that establishes a relationship between the perfect-square trinomial and the givens notable products.
So, we are looking for a notable product that gives us a value of "m" that is the coefficient of the linear term (x) and it's also the constant term.
- Trying with the two first options, we have:
[tex](x+1)^{2}=x^{2}+2x+ 1\\\\(x-1)^{2}=x^{2}-2x+ 1[/tex]
We can see that for these first two options, the value of m has not the same value for the coefficient of the linear term and the constant term since m is equal 2 and the constant number is not 2.
- Trying with the third option, we have:
[tex](x+2)^{2}=x^{2}+2*(2*x)+2^{2}=x^{2} +4x+4[/tex]
Now, we can see that the value of m is the same for the coefficient of the linear term and the constant term, we can see that m is equal to 4.
So, the correct option is the third option, because
[tex]m=4[/tex]
[tex]x^{2} +mx+m=(x+2)^{2}=x^{2} +4x+4=x^{2} +mx+m[/tex]
Have a nice day!
