Question

Factorise x^2/4-y^2/4​

Answer 1

`\large\boxed{\left((x)/(2)-(y)/(2)\right)\left((x)/(2)+(y)/(2)\right)=(x-y)/(2)\cdot(x+y)/(2)}`

Explanation:

`(x^2)/(4)-(y^2)/(4)=(x^2)/(2^2)-(y^2)/(2^2)\qquad\text{use}\ \left((a)/(b)\right)^n=(a^n)/(b^n)\\\\=\left((x)/(2)\right)^2-\left((y)/(2)\right)^2\qquad\text{use}\ (a-b)(a+b)=a^2-b^2\\\\=\left((x)/(2)-(y)/(2)\right)\left((x)/(2)+(y)/(2)\right)=(x-y)/(2)\cdot(x+y)/(2)`