Given:
The equation is:
[tex](2x+3y)(2x-3y)=4x^2+6y^2[/tex]
To find:
The error in the given equation and correct it.
Solution:
We have,
[tex](2x+3y)(2x-3y)=4x^2+6y^2[/tex]
Taking left-hand side, we get
[tex]L.H.S.=(2x+3y)(2x-3y)[/tex]
[tex]L.H.S.=(2x)^2-(3y)^2[/tex] [tex][\because a^2-b^2=(a-b)(a+b)][/tex]
[tex]L.H.S.=(2)^2(x)^2-(3)^2(y)^2[/tex] [tex][\because (ab)^x=a^xb^x][/tex]
[tex]L.H.S.=4x^2-9y^2[/tex]
It is not equal to right-hand side [tex]4x^2+6y^2[/tex]. In the right hand side, there must be a negative sign instead of positive sign.
Therefore, [tex](2x+3y)(2x-3y)=4x^2-6y^2[/tex].
