Question

Rút gọn:

(1/2a+b)³ + (1/2a-b)³

Answer 1

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

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

Answer 2

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

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