Question

1) Rút gọn các biểu thức sau:

a) \(\left(2x+1\right)^2+2\left(4x^2-1\right)+\left(2x-1\right)^2\)

b) \(\left(x^2-1\right)\left(x+2\right)-\left(x-2\right)\left(x^2+2x+4\right)\)

c) \(\left(3x-1\right)^2+2\left(3x-1\right)\left(2x+1\right)+\left(2x+1\right)^2\)

d) \(\left(x^2+1\right)\left(x-3\right)-\left(x-3\right)\left(x^2+3x+9\right)\)

e) \(\left(2x+3\right)^2+\left(2x+5\right)^2-2\left(2x+3\right)\left(2x+5\right)\)

f) \(\left(x-3\right)\left(x+3\right)-\left(x-3\right)^2\)

g) \(\left(3x+5\right)^2+\left(3x-5\right)^2-\left(3x+2\right)\left(3x-2\right)\)

h) \(\left(x-1\right)^3-\left(x+2\right)\left(x^2-2x+4\right)+3x^2-2x\)

i) \(\left(x^2-1\right)^3-\left(x^4+x^2+1\right)\left(x^2-1\right)\)

k) \(\left(x-1\right)^3-4x\left(x+1\right)\left(x-1\right)+3\left(x-1\right)\left(x^2+x+1\right)\)

Answer 1

a: =(2x+1+2x-1)^2=(4x)^2=16x^2

h: =x^3-3x^2+3x-1-x^3-8+3x^2-2x=x-9

g: =9x^2+30x+25+9x^2-30x+25-9x^2+4=9x^2+46

c: =(3x-1+2x+1)^2=25x^2

i: =x^6-3x^4+3x^2-1-x^6+1=-3x^4+3x^2