Question

rút gọn:

a, ( 1/2a + b)^3 + (1/2a - b )^3

b, ( x - 3 )^3 - ( x + 3 )^3

Answer 1

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

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

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

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

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

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

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