Question

Rút gọn các biểu thức sau

A.(2x+1)^2-(2x+1)(2x-1)

B.(4x+3)(x-1)-2x (2x+1 )

C.(2x+3)^2-(4x+1)(x+5)

D.(x+2)^3-(x-1)(x^2+x+1)

E.(x+2)(x^2-2x+1)-(x+3)(x-3)

F.(x+3)(x^2-3x+9)-(x^2+2x+4)(x-2)

Answer 1

a)

$(2x+1)^2-(2x+1)(2x-1)=(2x+1)[(2x+1)-(2x-1)]$

$=2(2x+1)$

b)

$(4x+3)(x-1)-2x(2x+1)=4x^2-x-3-4x^2-2x=-3x-3=-3(x+1)$

c)

$(2x+3)^2-(4x+1)(x+5)=(4x^2+12x+9)-(4x^2+21x+5)$

$=-9x+4$

Answer 2

d)

$(x+2)^3-(x-1)(x^2+x+1)=(x^3+6x^2+12x+8)-(x^3-1)$

$=6x^2+12x+9$

e)

$(x+2)(x^2-2x+1)-(x+3)(x-3)=(x^3-3x+2)-(x^2-9)$

$=x^3-x^2-3x+11$

f)

$(x+3)(x^2-3x+9)-(x^2+2x+4)(x-2)$

$=x^3+3^3-(x^3-2^3)=3^3+2^3=35$