Maths problems (F.3)

1) (2y2 + 5y + 1)(2y2 + 5y - 6) - 8
Let u = 2y2 + 5y
(u + 1)(u - 6) - 8
= u2 - 5u - 6 - 8
= u2 - 5u - 14
= (u - 7)(u + 2)
= (2y2 + 5y - 7)(2y2 + 5y + 2)
= (2y + 7)(y - 1)(2y + 1)(y + 2)
2) 4(4x2 - 12xy + 9y2) - 25(9y2 + 24yz + 16z2)
= 4(4x2 - 6xy - 6xy + 9y2) - 25(9y2 + 12yz + 12yz + 16z2)
= 4[2x(2x - 3y) - 3y(2x - 3y)] - 25[3y(3y + 4z) + 4z(3y + 4z)]
= 4(2x - 3y)2 - 25(3y + 4z)2
= (4x - 6y)2 - (15y + 20z)2
= (4x - 6y + 15y + 20z)(4x - 6y - 15y - 20z)
= (4x + 9y + 20z)(4x - 21y - 20z)
3) (16x4 - 16x2 + 4) - 49x2
= 16x4 - 8x2 - 8x2 + 4 - 49x2
= 4x2(4x2 - 2) - 2(4x2 - 2) - 49x2
= (4x2 - 2)2 - (7x)2
= (4x2 + 7x - 2)(4x2 - 7x - 2)
= (4x - 1)(x + 2)(4x + 1)(x - 2)