Rút gọn biểu thức: a) (x + y)^2 + (x − y)^2 b) (x + y)^2 − (x − y)^2 c) (x + 2)^2 − 2(x + 2)(x − 3) + (x − 3)^2
Rút gọn biểu thức:
a) (x + y)2 + (x − y)2
b) (x + y)2 − (x − y)2
c) (x + 2)2 − 2(x + 2)(x − 3) + (x − 3)2
Lời giải
a) (x + y)2 + (x − y)2
= (x2 + 2xy + y2) + (x2 − 2xy + y2)
= x2 + 2xy + y2 + x2 − 2xy + y2
= 2x2 + 2y2.
b) (x + y)2 − (x − y)2
= (x2 + 2xy + y2) − (x2 − 2xy + y2)
= x2 + 2xy + y2 − x2 + 2xy − y2
= 4xy.
c) (x + 2)2 − 2(x + 2)(x − 3) + (x − 3)2
= (x + 2 − x + 3)2
= 52 = 25.