中二簡單identities

To expand the expression:

Identity used: (u + v)(u - v) = u^2 - v^2

1.
(n + p)(n - p + 3)
= (n + p)[(n - p) + 3]
= (n + p)(n - p) + (n + p)3
= n^2 - p^2 + 3n + 3p ...... (answer)


2.
2(2q + r)(2q - r + 1)
= 2(2q + r)[(2q - r) + 1]
= 2(2q + r)(2q - r) + 2(2q + r)
= 2(4p^2 - r^2) + 4q + 2r
= 8p^2 - 2r^2 + 4q + 2r ...... (answer)


3.
(q-1)(1+q-2q^3)
= (q - 1)[(q + 1) - 2q^3]
= (q - 1)(q + 1) - (q - 1)q^3
= q^2 - 1 - q^4 + q^3
= -q^4 + q^3 + q^2 - 1 ...... (answer)