Answer:
[tex]4\, (u + 5)\, (u - 5)[/tex].
Step-by-step explanation:
Make use of the fact that the difference of two perfect squares, [tex](x^{2} - y^{2})[/tex], could be rewritten as a product of the form [tex](x + y)\, (x - y)[/tex]. That is:
[tex]x^{2} - y^{2} = (x + y)\, (x - y)[/tex].
In this question, the two squares are [tex](2\, u)^{2}[/tex] and [tex]10^{2}[/tex], respectively. Thus:
[tex]\begin{aligned}& 4\, u^{2} - 100 \\=\; & (2\, u)^{2} - (10)^{2} \\ =\; & (2\, u + 10) \, (2\, u - 10) \end{aligned}[/tex].
Simplify this expression even further:
[tex]\begin{aligned} & (2\, u + 10) \, (2\, u - 10) \\ =\; & (2\, (u + 5))\, (2\, (u - 5)) \\ =\; & 4\, (u + 5)\, (u - 5)\end{aligned}[/tex].
