Question

Bài 1.Rút gọn các biểu thức sau:

E=(2x+5)²-5(x-4)(x+4)-3(x-2)³

F=(2x-3)³-4(2x+4)² +3(x+3)(x²-3x+9)

G=(2x+1)²-3(x+2)(x²-2x+4)+(x+3)³

Answer 1

Bài 1:

a) Ta có: \(E=\left(2x+5\right)^2-5\left(x-4\right)\left(x+4\right)-3\left(x-2\right)^3\)

\(=4x^2+20x+25-5\left(x^2-16\right)-3\left(x^3-6x^2+12x-8\right)\)

\(=4x^2+20x+25-5x^2+60-3x^3+18x^2-36x+24\)

\(=-3x^3+17x^2-16x+109\)

b) Ta có: \(F=\left(2x-3\right)^3-4\left(2x+4\right)^2+3\left(x+3\right)\left(x^2-3x+9\right)\)

\(=8x^3-36x^2+54x-27-4\left(4x^2+16x+16\right)+3\left(x^3+27\right)\)

\(=8x^3-36x^2+54x-27-16x^2-64x-64+3x^3+81\)

\(=11x^3-52x^2-10x-10\)

c) Ta có: \(G=\left(2x+1\right)^2-3\left(x+2\right)\left(x^2-2x+4\right)+\left(x+3\right)^3\)

\(=4x^2+4x+1-3\left(x^3+8\right)+x^3+9x^2+27x+27\)

\(=x^3+13x^2+31x+28-3x^3-24\)

\(=-2x^3+13x^2+31x+4\)