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`a,`
`64x^4 + 81`
`= 64x^4 + 144x^2 + 81 - 114x^2`
`= (8x^2)^2 + 2 . 8x^2 . 9 + 9^2 - (12x)^2`
`= (8x^2 + 9)^2 - (12x)^2`
`= (8x^2 -12x+9) (8x^2 +12x+9)`
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`b,`
`x^8 + 4y^4`
`= x^8 + 4x^4y^2 + 4y^4 - 4x^4y^2`
`= (x^4)^2 + 2 . x^4 . 2y^2 + (2y^2)^2 - (2x^2y)^2`
`= (x^4 + 2y^2)^2 - (2x^2y)^2`
`= (x^4 + 2y^2 - 2x^2y) (x^4 + 2y^2 + 2x^2y)`
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`c,`
`x^8 + x^7 + 1`
`= (x^8 + x^7 + x^6) - (x^6 - 1)`
`= x^6 (x^2 + x + 1) - [(x^3)^2 - 1^2]`
`= x^6 (x^2 +x+1) - (x^3 - 1) (x^3 + 1)`
`= x^6 (x^2 +x+1) - (x - 1) (x^2 + x + 1) (x^3 + 1)`
`= x^6 (x^2 + x+1) - (x-1) (x^2 + x+1)`
`= (x^2 +x+1) [x^6 - (x-1) (x^3 +1)]`
`= (x^2 +x+1) [x^6 - (x^4 +x-x^3-1)]`
`= (x^2 +x+1) (x^6 - x^4 +x^3 - x+1)`
