To get the missing terms, we must completely factorize the Left Hand Side of the Equation.
We can do this in two different ways
Method 1
[tex]100x^{2} -36= 4(25x^{2} -9)}[/tex]
[tex]\Rightarrow 100x^{2} -36= 4((5x)^{2} -3^2)}[/tex]
Using difference of two squares we have
[tex]\Rightarrow 100x^{2} -36= 4(5x+3)(5x-3)}[/tex]
By comparing to the given equation, the missing term is
[tex]3[/tex]
Method 2
[tex]100x^{2} -36[/tex]
[tex]\Rightarrow 100x^{2} -36= (10x)^{2} -6^{2}[/tex]
Recall and apply the difference of two squares formula, to obtain,
[tex] 100x^{2} -36=(10x+6)(10x-6)[/tex]
We can still further factor 2 out of each factor to get,
[tex]100x^{2} -36=2(5x+3) \times 2(5x-3)[/tex]
[tex]\Rightarrow 100x^{2} -36=2\times2(5x+3)(5x-3)[/tex]
[tex]\Rightarrow 100x^{2} -36=4(5x+3)(5x-3)[/tex]
By comparing to the given equation, the missing term is
[tex]3[/tex]
