Answer:
[tex]9\, w^{2} - 100 = (3\, w - 10) \, (3\, w + 10)[/tex].
Step-by-step explanation:
Fact:
[tex]\begin{aligned} & (a - b)\, (a + b)\\ =\; & a^{2} + a\, b - a\, b - b^{2} \\ =\; & a^{2} - b^{2} \end{aligned}[/tex].
In other words, [tex](a^{2} - b^{2})[/tex], the difference of two squares in the form [tex]a^{2}[/tex] and [tex]b^{2}[/tex], could be factorized into [tex](a - b)\, (a + b)[/tex].
In this question, the expression [tex](9\, w^{2} - 100)[/tex] is the difference between two terms: [tex]9\, w^{2}[/tex] and [tex]100[/tex].
- [tex]9\, w^{2}[/tex] is the square of [tex]3\, w[/tex]. That is: [tex](3\, w)^{2} = 9\, w^{2}[/tex].
- On the other hand, [tex]10^{2} = 100[/tex].
Hence:
[tex]9\, w^{2} - 100 = (3\, w)^{2} - (10)^{2}[/tex].
Apply the fact that [tex]a^{2} - b^{2} = (a - b) \, (a + b)[/tex] to factorize this expression. (In this case, [tex]a = 3\, w[/tex] whereas [tex]b = 10[/tex].)
[tex]\begin{aligned}& 9\, w^{2} - 100 \\ =\; & (3\, w)^{2} - (10)^{2} \\ = \; & (3\, w - 10)\, (3\, w + 10)\end{aligned}[/tex].
