Question

rút gọn biểu thức

a.(x^2-2x+2)(x-2)(x^2+2x+2)(x+2)

b.(x+1)^3+(x-1)^3+x^3-3x(x+1)(x-1)

c.(x+y+z)^2+(x+y-z)^2+(2x-y)^2

d.100^2-99^2+98^2-97^2+...+2^2-1^2

Answer 1

a: \(\left(x^2-2x+2\right)\left(x^2+2x+2\right)\left(x-2\right)\left(x+2\right)\)

\(=\left[\left(x^2+2\right)^2-4x^2\right]\left(x^2-4\right)\)

\(=\left(x^3+2x\right)^2-4\left(x^2+2\right)^2-4x^4+16x^2\)

\(=x^6+4x^4+4x^2-4x^4+16x^2-4\left(x^4+4x^2+4\right)\)

\(=x^6+20x^2-4x^4-16x^2-16\)

\(=x^6-4x^4+4x^2-16\)

b: \(=x^3+3x^2+3x+1+x^3-3x^2+3x-1+x^3-3x\left(x^2-1\right)\)

\(=3x^3+6x-3x^3+3x\)

=9x

d: \(=\left(100-99\right)\left(100+99\right)+\left(98-97\right)\left(98+97\right)+...+\left(2-1\right)\left(2+1\right)\)

\(=100+99+...+2+1\)

=5050