Question

Simplify : (√x + √y ) (√x − √y) (x + y)(x2 + y2)

Answer 1

`Solution, \mathrm{Expand}\::\left(√(x)+√(y)\right)\left(√(x)-√(y)\right)\left(x+y\right)\left(x^2+y^2\right):\quad :x^4-:y^4`

`Steps:`

`\mathrm{Expand}\:\left(√(x)+√(y)\right)\left(√(x)-√(y)\right):\quad x-y, =\left(x-y\right)\left(x+y\right)\left(x^2+y^2\right)`

`\mathrm{Expand}\:\left(x-y\right)\left(x+y\right):\quad x^2-y^2, =:\left(x^2-y^2\right)\left(x^2+y^2\right)`

`\mathrm{Expand}\:\left(x^2-y^2\right)\left(x^2+y^2\right):\quad x^4-y^4, =:\left(x^4-y^4\right)`

`\mathrm{Expand}\::\left(x^4-y^4\right):\quad :x^4-:y^4, =:x^4-:y^4`

The correct answer is
`x^4-y^4`

Hope this helps!!!