\(a,4x^2-4x+1-y^2-8y-16\\ =\left(4x^2-4x+1\right)-\left(y^2+8y+16\right)\\ =\left(2x-1\right)^2-\left(y+4\right)^2\\ =\left(2x-1-y-4\right)\left(2x-1+y+4\right)\\ =\left(2x-y-5\right)\left(2x+y+3\right)\\ b,\left(x^2+1\right)^2-4x^2\\ =\left(x^2+1\right)^2-\left(2x\right)^2\\ =\left(x^2-2x+1\right)\left(x^2+2x+1\right)\\ =\left(x-1\right)^2\left(x+1\right)^2\\ c,?\)
`a, 4x^2 - 4x + 1 - y^2 - 8y - 16`
`= (4x^2 - 4x + 1)-(y^2 + 8y + 16)`
`= (2x - 1)^2 - (y + 4)^2`
`= (2x -1 - y - 4)(2x - 1 + y + 4)`
`= (2x - y - 5)(2x + y + 3)`
`b, (x^2 + 1)^2 - 4x^2`
`= (x^2 + 1)^2 - (2x)^2
`=(x^2 + 2x + 1)(x^2-2x+1)`
`= (x + 1)^2(x-1)^2`
`c, x^2 - y^2 + 10 - 6y + 16`
`= (x + 5)^2 - (y + 3)^2`
`= (x +5 + y + 3)(x + 5 - y - 3)`
`= (x+y+8)(x-y+2)`
a) 4x² - 4x + 1 - y² - 8y - 16
= (4x² - 4x + 1) - (y² + 8y + 16)
= (2x - 1)² - (y + 4)²
= (2x - 1 - y - 4)(2x - 1 + y + 4)
= (2x - y - 5)(2x + y + 3)
b) (x² + 1)² - 4x²
= (x² + 1)² - (2x)²
= (x² + 1 - 2x)(x² + 1 + 2x)
= (x - 1)²(x + 1)²
= (x² - 1)²