Factorise \frac{ {x}^(2) }{4} - \frac{ {y}^(2) }{4} ​

Question

Factorise

`\frac{ {x}^(2) }{4} - \frac{ {y}^(2) }{4}`
​

Answer 1

1/4(x+y)(x-y)

Explanation:

We can first factor out the shared 1/4 and it now looks like,

1/4(x^2-y^2)

Since x^2-y^2 is a difference of squares, which is a^2-b^2 = (a+b)(a-b), we can change x^2-y^2 to (x+y)(x-y). So our answer is:

1/4(x+y)(x-y)