Rút gọn biểu thức:
a/ (x2+2)2 - (x+2)(x-2)(x2+4)
= (x2+2)2- (x2-22)(x2+4)
= (x2+2)2- (x2-4)(x2+4)
=(x2+2)2- (x4- 42)
= x4+4x2+4-x4+16
= 4x2+20
=4(x2+5)
b/ (x+2y)2-(x-2y)2
= x2+4xy+4y2-x2+4xy-y2
= 8xy
A. \(\left(x^2+2\right)^2-\left(x+2\right)\left(x-2\right)\left(x^2+4\right)\)
\(=\left(x^4+4x^2+4\right)-\left[\left(x^2-4\right)\left(x^2+4\right)\right]\)
\(=\left(x^4+4x^2+4\right)-\left(x^4+4x^2-4x^2-16\right)\)
\(=x^4+4x^2+4-x^4-4x^2+4x^2+16\)
\(=4x^2+20\)
B. \(\left(x+2y\right)^2-\left(x-2y\right)^2\)
\(=\left(x^2+4xy+4y^2\right)-\left(x^2-4xy+4y^2\right)\)
\(=x^2+4xy+4y^2-x^2+4xy-4y^2\)
\(=6xy\)
