Answer:
Yes
Step-by-step explanation:
If [tex]a>b[/tex], then [tex]a-b>0[/tex].
If [tex]a,b[/tex] are positive, then [tex]a+b>0[/tex].
So if I multiply both sides of [tex]a-b>0[/tex] by [tex](a+b)[/tex] it will not effect the direction of the inequality since it is of positive value.
This actions gives us [tex](a+b)(a-b)>0[/tex].
Using foil we can multiply the left hand side out resulting in:
[tex]a^2-ba+ab-b^2>0[/tex]
[tex]a^2-b^2>0[/tex]
Add [tex]b^2[/tex] on both sides:
[tex]a^2>b^2[/tex].
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Also consider the function [tex]f(x)=x^2[/tex]. This function increases after [tex]x[/tex] is 0. This means as you increase the value for [tex]x[/tex] the value for [tex]x^2[/tex] increases for positive value inputs of [tex]x[/tex].
