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a) ( a + 4 ) 3 . b) ( 2 – b ) 3 .
c) ( m − 2 ) 2 − 2 3 . d) 2 a 3 − 2 b 3 .
a)
=(x-2)3
b)\(\left(2-x\right)^3\)
c)\(\left(x+\dfrac{1}{3}\right)^3\)
d)\(\left(\dfrac{x}{2}+y\right)^3\)
e)
\(=\left(x-1\right)^2\left(x-1-15\right)+25\left[3\left(x-1\right)-5\right]\)
\(=\left(x-1\right)^2\left(x-16\right)+25\left(3x-3-5\right)\)
\(=\left(x-1\right)^2\left(x-16\right)+25\left(3x-8\right)\)
\(B=\left(\frac{x}{2}+y\right)^3-6\left(\frac{x}{2}+y\right)^2.z+6\left(x+2y\right)z^2-8z^3\)
\(=\left(\frac{x}{2}+y\right)^3-3.\left(\frac{x}{2}+y\right)^2.2z+3.\left(\frac{x}{2}+y\right).\left(2z\right)^2-\left(2z\right)^3\)
\(=\left(\frac{x}{2}+y-2z\right)^3\)
\(C=\left(m-n\right)^3+15\left(m-n\right)^2.\left(m-p\right)-75\left(n-m\right)\left(p-m\right)^2-125\left(p-m\right)^3\)
\(=\left(m-n\right)^3+3.\left(m-n\right).\left[5\left(m-p\right)\right]+3.\left(m-n\right).\left[5\left(m-p\right)\right]^2+\left[5\left(m-p\right)\right]^3\)
\(=\left(m-n+5m-5p\right)^3=\left(6m-n-5p\right)^3\)
\(=\left(\dfrac{2}{3}a\right)^3-3.\left(\dfrac{2}{3}\right)^2a^2.2b+3.\dfrac{2}{3}a.4b^2-\left(2b\right)^3=\left(\dfrac{2}{3}a-2b\right)^3\)
b,\(\dfrac{4}{9}x^2+4x+9=\left(\dfrac{2}{3}x\right)^2+2.\dfrac{2}{3}x.3+3^2=\left(\dfrac{2}{3}x+3\right)^2\)
c, \(x^3+9x^2+27x+27=x^3+3.x^2.3+3.x.3^2+3^3=\left(x+3\right)^3\)
d, \(\dfrac{1}{8}-\dfrac{3}{4}x+\dfrac{3}{2}x^2-x^3=\left(\dfrac{1}{2}\right)^3-3.\left(\dfrac{1}{2}\right)^2.x+3.\dfrac{1}{2}.x^2-x^3=\left(\dfrac{1}{2}-x\right)^3\)
TK MIK 
b)\(27-10\sqrt{2}=5^2-2.5\sqrt{2}+2=\left(5-\sqrt{2}\right)^2\)
c)\(18-8\sqrt{2}=4^2-2.4\sqrt{2}+2=\left(4-\sqrt{2}\right)^2\)
d)\(4-2\sqrt{3}=3-2\sqrt{3}+1=\left(\sqrt{3}-1\right)^2\)
e)\(6\sqrt{5}+14=9+2.3\sqrt{5}+5=\left(3+\sqrt{5}\right)^2\)
f)\(20\sqrt{5}+45=5^2+2.5.2\sqrt{5}+20=\left(5+2\sqrt{5}\right)^2\)
g)\(7-2\sqrt{6}=6-2\sqrt{6}+1=\left(\sqrt{6}-1\right)^2\)
Bài làm:
Ta có: \(\frac{x^3}{8}+\frac{3}{4}x^2y^2+\frac{3}{2}xy^4+y^6\)
\(=\left(\frac{x}{2}\right)^3+3.\left(\frac{x}{2}\right)^2.y^2+3.\frac{x}{2}.\left(y^2\right)^2+\left(y^2\right)^3\)
\(=\left(\frac{x}{2}+y^2\right)^3\)
\(\left(m-n\right)^6-6\left(m-n\right)^4+12\left(m-n\right)^2-8=\left[\left(m-n\right)^2-2\right]^3\)
\(\dfrac{8}{27}a^3-\dfrac{8}{3}a^2b+8b^2a-8b^3=\left(\dfrac{2}{3}a-2b\right)^3\)
Chúc bạn học tốt !!