Question

Rút gọn biểu thức:

a) (2x+5)²+(2x-5)²-(2x-1)(2x+1)

b) (2a+b)³+(2a-b)³-16a³

c) (2x-1)³-(x-2)(x²+2x+4)-7x³-2x

d) (x+1)²-(x-1)²-3(x+1)(x-1)

e) (x²+2)²-(x-2)(x+2)(x²+4)

Answer 1

a: \(=4x^2+20x+25+4x^2-20x+25-\left(4x^2-1\right)\)

\(=8x^2+50-4x^2+1=4x^2+51\)

b: \(=8a^3+12a^2b+6ab^2+b^3+8a^3-12a^2b+6ab^2-b^3-16a^3\)

\(=12ab^2\)

c: \(\left(2x-1\right)^3-\left(x-2\right)\left(x^2+2x+4\right)-7x^3-2x\)

\(=\left(2x-1\right)^3-x^3+8-7x^3-2x\)

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

\(=-12x^2+4x+7\)

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

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

\(=x^2+2x+1-x^2+2x-1-3x^2+3\)

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