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
\(100x^{2} -36= 4(25x^{2} -9)}\)
\(\Rightarrow 100x^{2} -36= 4((5x)^{2} -3^2)}\)
Using difference of two squares we have
\(\Rightarrow 100x^{2} -36= 4(5x+3)(5x-3)}\)
By comparing to the given equation, the missing term is
\(3\)
Method 2
\(100x^{2} -36\)
\(\Rightarrow 100x^{2} -36= (10x)^{2} -6^{2}\)
Recall and apply the difference of two squares formula, to obtain,
\(100x^{2} -36=(10x+6)(10x-6)\)
We can still further factor 2 out of each factor to get,
\(100x^{2} -36=2(5x+3) \times 2(5x-3)\)
\(\Rightarrow 100x^{2} -36=2\times2(5x+3)(5x-3)\)
\(\Rightarrow 100x^{2} -36=4(5x+3)(5x-3)\)
By comparing to the given equation, the missing term is
\(3\)
