Toán Lớp 8: Thu gọn đa thức A = (ax + by + cz)2 + (ay – bx)2 + (az – cx)2 + (bz – cy)2 ta được A. (x2 + y2 + z2) + (a2 + b2 + c2) B. (x2 + y2 + z2)

Question

Toán Lớp 8:  Thu gọn đa thức A = (ax + by + cz)2 + (ay – bx)2 + (az – cx)2 + (bz – cy)2 ta được A. (x2 + y2 + z2) + (a2 + b2 + c2) B. (x2 + y2 + z2)(a2 + b2 + c2) C. (x2 + y2 + z2)(a + b + c)2        D. (x + y + z)(a2 + b2 + c2)

thanhtung · Answer

Giải đáp: Chọn B : (x&sup2; + y&sup2; + z&sup2;)(a&sup2; + b&sup2; + c&sup2;)       Lời giải và giải thích chi tiết:    A = (ax + by + cz)&sup2; + (ay - bx)&sup2; + (az - cx)&sup2; + (bz - cy)&sup2;       = a&sup2;x&sup2; + b&sup2;y&sup2; + c&sup2;z&sup2; + 2acxz + 2abxy + 2bcyz + a&sup2;y&sup2; - 2abxy + b&sup2;x&sup2; + a&sup2;z&sup2; - 2acxz + c&sup2;x&sup2; + b&sup2;z&sup2; - 2bcyz + c&sup2;y&sup2;      = a&sup2;x&sup2; + b&sup2;y&sup2; + c&sup2;z&sup2; + a&sup2;y&sup2; + b&sup2;x&sup2; + a&sup2;z&sup2; + c&sup2;x&sup2; + b&sup2;z&sup2; + c&sup2;y&sup2;     = (a&sup2;x&sup2; + a&sup2;y&sup2; + a&sup2;z&sup2;) + (b&sup2;x&sup2; + b&sup2;y&sup2; + b&sup2;z&sup2;) + (c&sup2;x&sup2; + c&sup2;y&sup2; + c&sup2;z&sup2;)     = a&sup2;(x&sup2; + y&sup2; + z&sup2;) + b&sup2;(x&sup2; + y&sup2; + z&sup2;) + c&sup2;(x&sup2; + y&sup2; + z&sup2;)     = (x&sup2; + y&sup2; + z&sup2;)(a&sup2; + b&sup2; + c&sup2;)

lanminhngoc · Answer

Giải đáp:     Giải đáp l&agrave;: B     Lời giải và giải thích chi tiết:    A = (ax + by + cz) 2  + (ay &ndash; bx) 2  + (az &ndash; cx) 2  + (bz &ndash; cy) 2      = a 2 x 2  + b 2 y 2  + c 2 z 2  + 2abxy + 2acxz + 2bcyz + a 2 y 2  &ndash; 2abxy + b 2 x 2  + a 2 z 2  &ndash; 2acxz + c 2 z 2  + b 2 z 2  &ndash; 2bczy + c 2 y 2      = a 2 x 2  + b 2 y 2  + c 2 z 2  + a 2 y 2  + b 2 x 2  + a 2 z 2  + c 2 x 2  + b 2 z 2  + c 2 y 2      = (a 2 x 2  + b 2 x 2  + c 2 x 2 ) + (b 2 y 2  + a 2 y 2  + c 2 y 2 ) + (b 2 z 2  + a 2 z 2  + c 2 z 2 )     = x 2 (a 2  + b 2  + c 2 ) + y 2 (a 2  + b 2  + c 2 ) + z 2 (a 2  + b 2  + c 2 )     = (x 2  + y 2  + z 2 )(a 2  + b 2  + c 2 )