Question

Rút gọn biểu thức:

a/ (x²+2)²-(x+2)(x-2)(x²+4)

b/ (x+2y)²-(x-2y)²

c/ 5(x+2)(x-2)-1/2(6-8x)²+17

Answer 1

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

Answer 2

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. \(\left(x+2y\right)^2-\left(x-2y\right)^2\)
\(=\left(x^2+4xy+4y^2\right)-\left(x^2-4xy+4y^2\right)\)
\(=x^2+4xy+4y^2-x^2+4xy-4y^2\)
\(=6xy\)