Question

2) c/m các biểu thức sau không phụ thuộc vào biến số

a) A=3.(x-1)²-(x+1)²+2(x-3) (x+3)-(2x+3)²-(5-20x)+5x(x-7) (x+7)-x.(2x-1)²-(x³+4x²-246x)-175

b) B=-2x.(3x+2)²+(4x+1)²+2(x³+8x²+3x-2)-(5-x)+(5x-2)²-(6x+1)²+11(x-2) (x+2)-16(3-2x) cần gắp

Answer 1

a: Đặt \(C=3\left(x-1\right)^2-\left(x+1\right)^2+2\left(x-3\right)\left(x+3\right)-\left(2x+3\right)^2-\left(5-20x\right)\)

\(D=5x\left(x-7\right)\left(x+7\right)-x\left(2x-1\right)^2-\left(x^3+4x^2-246x\right)-175\)

Do đó: A=C+D

\(C=3\left(x-1\right)^2-\left(x+1\right)^2+2\left(x-3\right)\left(x+3\right)-\left(2x+3\right)^2-\left(5-20x\right)\)

\(=3x^2-6x+3-x^2-2x-1+2x^2-18-\left(4x^2+12x+9\right)-5+20x\)

\(=4x^2-8x-16-4x^2-12x-9-5+20x\)

\(=-30\)

\(D=5x\left(x-7\right)\left(x+7\right)-x\left(2x-1\right)^2-\left(x^3+4x^2-246x\right)-175\)

\(=5x\left(x^2-49\right)-x\left(4x^2-4x+1\right)-x^3-4x^2+246x-175\)

\(=5x^3-245x-4x^3+4x^2-x-x^3-4x^2+246x-175\)

=-175

A=C+D=-30-175=-205

b: Đặt \(E=-2x\left(3x+2\right)^2+\left(4x+1\right)^2+2\left(x^3+8x^2+3x-2\right)-\left(5-x\right)\)

\(F=\left(5x-2\right)^2-\left(6x+1\right)^2+11\left(x-2\right)\left(x+2\right)-16\left(3-2x\right)\)

Do đó: B=E+F

\(E=-2x\left(3x+2\right)^2+\left(4x+1\right)^2+2\left(x^3+8x^2+3x-2\right)-\left(5-x\right)\)

\(=-2x\left(9x^2+12x+4\right)+16x^2+8x+1+2x^3+16x^2+6x-4-5+x\)

\(=-18x^3-24x^2-8x+32x^2+14x+1-5+x\)

\(=-18x^3+8x^2+7x-4\)

\(F=\left(5x-2\right)^2-\left(6x+1\right)^2+11\left(x-2\right)\left(x+2\right)-16\left(3-2x\right)\)

\(=25x^2-20x+4-36x^2-12x-1+11x^2-44-48+32x\)

\(=-95\)

\(B=-18x^3+8x^2+7x-99\)