中二簡單factorization~~~

1.8q^2 + 2r + 4q - 2r^2
= 2[4q^2 + 2q + 1/4 - 1/4 + r - r^2]
= 2[(2q + 1/2)^2 - (r - 1/2)^2]
= 2(2q + 1/2 + r - 1/2)(2q + 1/2 - r + 1/2)
= 2(2q + r)(2q - r + 1)
2. -2q^4 + 2q^3 + q^2 - 1
= -2q^3(q - 1) + (q - 1)(q + 1)
= (q - 1)(-2q^3 + q + 1)
= (q - 1)(-2q^3 + 2q^2 - 2q^2 + 2q - q + 1)
= (q - 1)[-2q^2(q - 1) - 2q(q - 1) - (q - 1)]
= -(q - 1)^2(2q^2 + 2q - 1)
3.b^2 + 4bc + 4c^2
= b^2 + 2bc + 2bc + 4c^2
= b(b + 2c) + 2c(b + 2c)
= (b + 2c)^2
4.36x^2 + 49y^2 + 84xy
= 36x^2 + 42xy + 42xy + 49y^2
= 6x(6x + 7y) + 7y(6x + 7y)
= (6x + 7y)^2
5. h^2 - 16hk + 64k^2
= h^2 - 8hk -8hk + 64k^2
= h(h - 8k) - 8k(h - 8k)
= (h - 8k)^2