Question

Which expression is a difference of squares?


9m$x^{4}$−49n$x^{6}$

100x$x^{2}$−10y$x^{4}$

32a$x^{2}$−81n$x^{2}$

16h$x^{2}$−21t$x^{10}$

Answer 1

If these are only integers, the answer is the first example.

However, each of these expressions can be represented as the difference of squares.

$9m^4-49n^6=3^2(m^2)^2-7^2(n^3)^2=(3m^2)^2-(7n^3)^2\\\\100x^2-10y^4=10^2x^2-(\sqrt{10})^2(y^2)^2=(10x)^2-(y^2\sqrt{10})^2\\\\32a^2-81n^2=(\sqrt{32})^2a^2-9^2n^2=(a\sqrt{32})^2-(9n)^2\\\\16h^2-21t^{10}=4^2h^2-(\sqrt{21})^2(t^5)^2=(4h)^2-(t^5\sqrt{21})^2$

Used:

$(a^n)^m=a^{nm}\\\\(ab)^n=a^nb^n\\\\(\sqrt{a})^2=a$