Question

Factor `b^(-2) - 25` over Real numbers?

Answer 1

`(1/b-5)(1/b+5)`

Explanation:

`b^-2-25=1/b^2-25`

`1/b^2-25" is a "color(blue)"difference of squares"`

`•color(white)(x)a^2-b^2=(a-b)(a+b)`

`"here "a=1/b" and "b=5`

`rArrb^-2-25=(1/b-5)(1/b+5)`

Answer 2

`b^-2(1-5b)(1+5b)`

Explanation:

`"take out a "color(blue)"common factor of "b^-2`

`b^-2(1-25b^2)`

`=b^-2(1-5b)(1+5b)larrcolor(blue)"difference of squares"`

`"as another possibility"`