Question

Factorise the following:

`(x - y/3)^2 - (49y^2)/9`

Answer 1

To factorise `(x - y/3)^2 - (49y^2)/9`, we can use the difference of squares formula.

The expression is in the form A² – B², where:

`A = (x - y/3)` and `B = (7y)/3`

Now, apply the difference of squares formula:

A² – B² = (A – B)(A + B)

Substitute A and B into the formula:

`(x - y/3 - (7y)/3)(x - y/3 + (7y)/3)`

Simplify both terms:

1. For A – B:

`x - y/3 - (7y)/3 = x - (8y)/3`

2. For A + B:

`x - y/3 + (7y)/3 = x + (6y)/3 = x + 2y`

Thus, the factorised form of `(x - y/3)^2 - (49y^2)/9 "is" (x - (8y)/3)(x + 2y)`