Answer:
[tex]a=\sqrt{c^2-b^2[/tex]
⇒ [tex]a=\sqrt{(c+b)(c-b)}[/tex] [Factorized form]
Step-by-step explanation:
Given expression:
[tex]a^2+b^2=c^2[/tex]
We need to make [tex]a[/tex] the subject.
In order to do that we need to solve the expression for [tex]a[/tex] in terms of [tex]b[/tex] and [tex]c[/tex]
We have,
[tex]a^2+b^2=c^2[/tex]
Subtracting both sides by [tex]b^2[/tex]
[tex]a^2+b^2-b^2=c^2-b^2[/tex]
[tex]a^2=c^2-b^2[/tex]
Taking square root both sides in order to remove square of [tex]a[/tex]
[tex]\sqrt{a^2}=\sqrt{c^2-b^2}[/tex]
[tex]a=\sqrt{c^2-b^2[/tex]
The difference of squares can be factorized and written as:
[tex]a=\sqrt{(c+b)(c-b)}[/tex] [difference of squares [tex]x^2-y^2=(x+y)(x-y)[/tex] ]
