Question

$125a {}^{2} -45b {}^{2}$

Answer 1

$\underline{\mathfrak{heya !!}} \\ \\</p> <p>125a^2 - 45b^2 \\ \\</p> <p>= (\sqrt{125} \: a)^2 - (\sqrt{45} \: b)^2 \\ \\</p> <p>= (\sqrt{5 \times 5 \times 5} \: a)^2 - (\sqrt{3 \times 3 \times 5} \: b)^2 \\ \\</p> <p>= (5 \sqrt{5} \: a)^2 - (3 \sqrt{5} \: b)^2 \\ \\</p> <p>\boxed{= (5 \sqrt{5} \: a + 3 \sqrt{5} \: b)(5 \sqrt{5} \: a - 3 \sqrt{5} \: b)} \\ \\</p> <p>\text{---[Using:- a^2 - b^2 = (a + b)(a - b) ]} \\ \\</p> <p>\underline{\mathfrak{hope it helps !!}}$