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`.