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Question
Factorise the following:
`(x - y/3)^2 - (49y^2)/9`
Sum
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Solution
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)`
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