please explain this
 

Asked by Padmini | 26th Mar, 2017, 04:14: PM

Expert Answer:

begin mathsize 16px style Hi space Roopa comma
In space the space first space step comma space we space use space the space identity comma space bold x to the power of bold 2 bold minus bold 2 bold xy bold plus bold y to the power of bold 2 bold equals bold left parenthesis bold x bold minus bold y bold right parenthesis to the power of bold 2
So comma space to space do space that comma space we space write space the space first space three space terms space of space the space expression space in space the space identity space form.
Since space 4 equals 2 squared space and space 9 equals 3 squared comma space we space write
4 straight a squared equals left parenthesis 2 straight a right parenthesis squared space and space 3 squared equals left parenthesis 9 right parenthesis squared
So comma space 4 straight a squared minus 12 ab plus 9 minus 49 straight b squared equals open square brackets left parenthesis 2 straight a right parenthesis squared minus left parenthesis 2 cross times 2 cross times 3 ab right parenthesis plus 3 squared close square brackets minus 49 straight b squared
We space are space going space to space use space bold x to the power of bold 2 bold plus bold 2 bold xy bold plus bold y to the power of bold 2 bold equals bold left parenthesis bold x bold plus bold y bold right parenthesis to the power of bold 2 space now space in space the space first space bracket.
4 straight a squared minus 12 ab plus 9 minus 49 straight b squared equals left parenthesis 2 straight a minus 3 right parenthesis squared minus 49 straight b squared equals left parenthesis 2 straight a minus 3 right parenthesis squared minus left parenthesis 7 straight b right parenthesis squared
In space the space next space step comma space we space are space going space to space use space the space identity space straight x squared minus straight y squared equals left parenthesis straight x minus straight y right parenthesis left parenthesis straight x plus straight y right parenthesis
where space straight x equals 2 straight a minus 3 space and space straight y equals 7 straight b
So comma space left parenthesis 2 straight a minus 3 right parenthesis squared minus left parenthesis 7 straight b right parenthesis squared equals left parenthesis 2 straight a minus 3 minus 7 straight b right parenthesis left parenthesis 2 straight a minus 3 plus 7 straight b right parenthesis

If space you space are space still space confused comma space let space me space know.
We space are space using space the space two space identities space to space factorize space the space expression.
Instead space of space straight a space and space straight b comma space straight I space have space taken space straight x space and space straight y space in space the space identities space to space avoid space confusion space with space the space expression space terms. end style

Answered by Rebecca Fernandes | 26th Mar, 2017, 07:11: PM