Use suitable identity to get each of the following products!

vi. (a^2 + b^2) (-a^2 + b^2)

how do i solve it!no identity is matching with this!

rosala
Dec 28, 2014

#1**+15 **

Best Answer

(a^2 + b^2) (-a^2 + b^2)

$$(a^2 + b^2) (-a^2 + b^2)\\\\

=(b^2 + a^2) (b^2 -a^2)\\\\$$

Now you can see that it is the difference of 2 squares. :)

so the answer is

$$\\=(b^2)^2-(a^2)^2\\\\

=b^4-a^4$$

Does that all makes sense Rosala ?

Melody
Dec 28, 2014

#2**+10 **

umm no...not to me right now!

how did you just swap everything ......i dont get it!

{i am talking about this step}(b^2 + a^2) (b^2 -a^2)

its like sorting out a ball of wool!

rosala
Dec 28, 2014

#3**+10 **

Okay rosala let's look at this.

a+b=b+a agreed? (1)

a-b=-b+a agreed? (2)

-b+a=a-b agreed? (It is the same as the one above only in reverse) (3)

so

$${{\mathtt{a}}}^{{\mathtt{2}}}{\mathtt{\,\small\textbf+\,}}{{\mathtt{b}}}^{{\mathtt{2}}} = {{\mathtt{b}}}^{{\mathtt{2}}}{\mathtt{\,\small\textbf+\,}}{{\mathtt{a}}}^{{\mathtt{2}}}$$ agreed? (4)

and

$${\mathtt{\,-\,}}{{\mathtt{a}}}^{{\mathtt{2}}}{\mathtt{\,\small\textbf+\,}}{{\mathtt{b}}}^{{\mathtt{2}}} = {{\mathtt{b}}}^{{\mathtt{2}}}{\mathtt{\,-\,}}{{\mathtt{a}}}^{{\mathtt{2}}}$$ agreed ? (5)

so

$$(a^2 + b^2) (-a^2 + b^2)=(b^2 + a^2) (b^2 -a^2)\\\\$$ agreed (6)

I have numbered all the lines so that you can tell me which ones don't make sense to you. :)

Melody
Dec 28, 2014