Question

Encuentra en cada producto notable el error o errores,enciérralo y escribe el resultado correcto.

Answer 1

Given:

The equation is:

$(2x+3y)(2x-3y)=4x^2+6y^2$

To find:

The error in the given equation and correct it.

Solution:

We have,

$(2x+3y)(2x-3y)=4x^2+6y^2$

Taking left-hand side, we get

$L.H.S.=(2x+3y)(2x-3y)$

$L.H.S.=(2x)^2-(3y)^2$                 $[\because a^2-b^2=(a-b)(a+b)]$

$L.H.S.=(2)^2(x)^2-(3)^2(y)^2$       $[\because (ab)^x=a^xb^x]$

$L.H.S.=4x^2-9y^2$

It is not equal to right-hand side $4x^2+6y^2$. In the right hand side, there must be a negative sign instead of positive sign.

Therefore, $(2x+3y)(2x-3y)=4x^2-6y^2$.