(m + n)2 − (p + q)2 + (m + p)2 − (n + q)2

is gelijk aan 		A.   4(m − q)2
B.   4(m + q)2
C.   2(m − q)(m + n + p)
D.   2(m − q)(m + 2n + p)
E.   2(m − q)(m + n + p + q)
A    B    C    D    E

[ 2,3-7779 - op net sinds 19.1.15-(E)-27.10.2023 ]

Translation in   E N G L I S H

(m + n)2 − (p + q)2 + (m + p)2 − (n + q)2

is equal to 		A.   4(m − q)2
B.   4(m + q)2
C.   2(m − q)(m + n + p)
D.   2(m − q)(m + 2n + p)
E.   2(m − q)(m + n + p + q)

Oplossing - Solution

1ste manier :
  (m + n)² −(p + q)² + (m + p)² − (n + q)²
= (m+n+p+q)(m+n−p−q) + (m+p+n+q)(m+p−n−q)
= (m+n+p+q)(m+n-p−q+m+p−n−q)
= (m+n+p+q)(2m−2q)
= 2(m − q)(m + n + p + q)
2de manier :
  (m + n)² − (n + q)² + (m + p)² − (p + q)²
= (m+n+n+q)(m+n−n−q) + (m+p+p+q)(m+p−p−q)
= (m+n+n+q)(m−q+m−q)
= (2m−2q)(m+n+n+q)
= 2(m − q)(m + n + p + q)