Factor the following expressions with the help of difference of squares formula
`x^8 - y^8` | `(x-y) (x+y) (x^2+y^2) (x^4+y^4)` | |
`(x + 5)^2/36 - (y - 5)^2/64` | `((x + 5)/6 - (y - 5)/8)((x + 5)/6 + (y - 5)/8)`, which can be simplified to `((4x + 3y + 5)(4x - 3y + 35))/576` | |
`sqrt(x^2 - 1)` | `sqrt((x + 1)(x - 1))` | |
`x^2/225 - y^2/100` | `(x/15 + y/10)(x/15 - y/10)` | |
`a^4b^2 - b^4a^2` | `(a^2b^2)(a + b)(a - b)` | |
`100x^2 - 324y^2` | `(10x + 18y)(10x - 18y)` | |
`8x^2 - 72y^2` | `8(x + 3y)(x - 3y)` | |
`(x + 1)^2 - (y - 1)^2` | `((x + 1) + (y - 1))((x + 1) - (y - 1))`, which can be simplified to `(x + y)(x - y + 2)` | |
`(a^2 - b^2)^2 - (a^2 + b^2)^2` | `((a^2 - b^2) + (a^2 + b^2))((a^2 - b^2) - (a^2 + b^2))`, which can be simplified to `-4a^2b^2` | |
`x^2/64 - 16y^2` | `(x/8 - 4y)(x/8 + 4y)` |
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