Question

Rút gọn biểu thức

a) 2X.(2X-1)^2-3X.(X+3)).(X-3)-4X.(X+1)^2

b) (a-b+c)^2-(b-c)^2+2ab-2ac

c) (3x+1)^2-2.(3x+1).(3x+5)+(3x+5)^2

Answer 1

a: \(=2x\left(4x^2-4x+1\right)-3x\left(x^2-9\right)-4x\left(x^2+2x+1\right)\)

\(=8x^3-8x^2+2x-3x^3+27x-4x^3-8x^2-4x\)

\(=x^3-16x^2+25x\)

b: \(=\left(a-b+c-b+c\right)\left(a-b+c+b-c\right)+2ab-2ac\)

\(=\left(a-2b+2c\right)\cdot a+2ab-2ac\)

\(=a^2-2ab+2ac+2ab-2ac=a^2\)

c: \(\left(3x+1\right)^2-2\left(3x+1\right)\left(3x+5\right)+\left(3x+5\right)^2\)

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