Question

Simplify:

[(b sq rt a) - (a sq rt b)]^2 using square formula

Answer 1

\[ (a \sqrt{b} - b \sqrt{a})^2\]

Answer 2

There is a rule: \(\large\color{black}{ (\color{blue}{c}+\color{red}{d} )^2= \color{blue}{c}^2+2\color{blue}{c}{\tiny~}\color{red}{d}+\color{red}{d}^2 }\)

Answer 3

in your case:
\(\large\color{black}{\color{blue}{c=a\sqrt{b} }\\ \color{red}{d = b\sqrt{a} } }\)

Answer 4

\[(x-y)^2 = x^2 -2xy+y^2\]

Answer 5

In this case: \(x= b\sqrt{a} ~,~ y=a\sqrt{b} \)

Answer 6

When you make the substitution, what do you get?

Answer 7

this is what I got so far:

=\[b^2a - 2*b \sqrt{a} * a \sqrt{b} + a^2b\]

Answer 8

Thats correct.

Answer 9

\[(b\sqrt{a})^2 = b^2a~, ~2(b\sqrt{a})(a\sqrt{b}) = 2ab\sqrt{ab}~,~ (a\sqrt{b})^2 = a^2b\]

Answer 10

\[-2(b\sqrt{a})(a\sqrt{b}) = -2ab\sqrt{ab}\]

Answer 11

I was right about that then! Thank you! I found it out not your way but by partializing ^^