Question

Bài 1. Rút gọn các biểu thức sau: a) A = (a + b) ^ 3 + (a - b) ^ 3 - 2a ^ 3 b) B = (2x - 1)(4x ^ 2 + 2x + 1) - 8(x + 2)(x ^ 2 - 2x + 4) , c) C = (x + 2y)(x ^ 2 - 2xy + 4y ^ 2) + (2x - y)(4x ^ 2 + 2xy + y ^ 2) - 9x ^ 3

Answer 1

a: \(A=\left(a+b\right)^3+\left(a-b\right)^3-2a^3\)

\(=a^3+3a^2b+3ab^2+b^3+a^3-3a^2b+3ab^2-b^3-2a^3\)

\(=6ab^2\)

b: \(B=\left(2x-1\right)\left(4x^2+2x+1\right)-8\left(x+2\right)\left(x^2-2x+4\right)\)

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

\(=8x^3-1-8x^3-64=-65\)

c: \(C=\left(x+2y\right)\left(x^2-2xy+4y^2\right)+\left(2x-y\right)\left(4x^2+2xy+y^2\right)-9x^3\)

\(=x^3+\left(2y\right)^3+\left(2x\right)^3-y^3-9x^3\)

\(=x^3+8y^3+8x^3-y^3-9x^3=7y^3\)