You may notice that the expression is a difference of squares, with [tex]100b^2[/tex] as one of the squares and [tex]144a^4[/tex] as the other square.
Now, we can apply the Difference of Squares formula:
[tex]a^2 - b^2 = (a - b)(a + b)[/tex]
In this case, we can say [tex]a^2 = 100b^2[/tex] and [tex]b^2 = 144a^4[/tex]. We are going to need to find [tex]a[/tex] and [tex]b[/tex]. To do this, we can take the square root of both sides of the prior two equations.
[tex]\sqrt{a^2} = \sqrt{100b^2}[/tex]
[tex]a = 10b[/tex]
[tex]\sqrt{b^2} = \sqrt{144a^4}[/tex]
[tex]b = 12a^2[/tex]
We can now use the equation to find our result:
[tex]100b^2 - 144a^4 = (10b - 12a^2)(10b + 12a^2)[/tex]
You can see that Choice C, or 10b + 12a² is a factor.
