Answer:
[tex]49a^{2} - 25b^{2} = (7a + 5b)(7a - 5b)[/tex]
Step-by-step explanation:
The most common factorization of binomial expressions are:
[tex](x + y)^{2} = x^{2} + 2xy + y^{2}[/tex]
[tex](x - y)^{2} = x^{2} - 2xy + y^{2}[/tex]
[tex](x + y)*(x - y) = x^{2} - y^{2}[/tex]
This goes both ways, that is, [tex](x + y)*(x - y) = x^{2} - y^{2}[/tex], just as, [tex]x^{2} - y^{2} = [tex](x + y)*(x - y)[/tex]
So
[tex]49a^{2} - 25b^{2} = (7a + 5b)(7a - 5b)[/tex]