Question

Bài 1: Rút gọn biểu thức:

a/ (6x+1)²+(6x-1)²-2(1+6x)(6x-1)

b/ 3(2²+1)(2⁴+1)(2⁸+1)(2¹⁶+1)

c/ x(2x³-3)-x²(5x+1)+x²

d/ 3x(x-2)-5x(1-x)-8(x²-3)

Bài 2: Tình gtri biểu thức A= (x-y)(x²+xy+y²)+2y³ tại x =\(\dfrac{2}{3}\) và y = \(\dfrac{1}{3}\)

Answer 1

Bài 1:

a) \(\left(6x+1\right)^2+\left(6x-1\right)^2-2\left(1+6x\right)\left(6x-1\right)\)

\(=36x^2+72x+1+36x^2-72x+1-2\left(36x^2-1\right)\)

\(=36x^2+72x+1+36x^2-72x+1-72x^2+2\)

\(=4\)

b) \(3\left(2^2+1\right)\left(2^4+1\right)\left(2^8+1\right)\left(2^{16}+1\right)\)

\(=\left(2^2-1\right)\left(2^2+1\right)\left(2^4+1\right)\left(2^8+1\right)\left(2^{16}+1\right)\)

\(=\left(2^4-1\right)\left(2^4+1\right)\left(2^8+1\right)\left(2^{16}+1\right)\)

\(=\left(2^8-1\right)\left(2^8+1\right)\left(2^{16}+1\right)\)

\(=\left(2^{16}-1\right)\left(2^{16}+1\right)\)

\(=2^{32}-1\)

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

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

\(=2x^4-5x^3-3x\)

d) \(3x\left(x-2\right)-5x\left(1-x\right)-8\left(x^2-3\right)\)

\(=3x^2-6x-5x+5x^2-8x^2+24\)

\(=-11x+24\)

Answer 2

Bài 2:

\(A=\left(x-y\right)\left(x^2+xy+y^2\right)+2y^3\)

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

\(=x^3+y^3\)

\(=\left(\dfrac{2}{3}\right)^3+\left(\dfrac{1}{3}\right)^3\)

\(=\dfrac{1}{3}\).