Question

Rút gọn :  ( \(\frac{1}{2}a+b\) )^3 + ( \(\frac{1}{2}a-\:b\) )^3

Answer 1

\(\left(\frac{1}{2}a+b\right)^3+\left(\frac{1}{2}a-b\right)^3\)

\(=\left[\left(\frac{1}{2}a+b\right)+\left(\frac{1}{2}a-b\right)\right].\left[\left(\frac{1}{2}a+b\right)^2-\left(\frac{1}{2}a+b\right).\left(\frac{1}{2}a-b\right)+\left(\frac{1}{2}a-b\right)^2\right]\)

Tới đấy phân tích ra là được nhé . Mình đang bận .

Answer 2

\(\left(\frac{1}{2}a+b\right)^3+\left(\frac{1}{2}a-b\right)^3\)

\(=\left(\frac{1}{2}a+b+\frac{1}{2}a-b\right)\left[\left(\frac{1}{2}a+b\right)^2-\left(\frac{1}{2}a+b\right)\left(\frac{1}{2}a-b\right)+\left(\frac{1}{2}a-b\right)^2\right]\)

\(=a\left(\frac{1}{4}a^2+ab+b^2-\frac{1}{4}a^2+b^2+\frac{1}{4a^2}-ab+b^2\right)\)

\(=a\left(\frac{1}{4}a^2+3b^2\right)\)

\(=\frac{1}{4}a^3+3ab^2\)