cho 8a^3-12a+10a-2013=0va 9b^3-9b^2+5b+669=0
tinh M=8a^3+27b^3+36ab
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a)\(\left(a^3-b^3\right)+\left(a-b\right)^2\)
\(=\left(a-b\right)\left(a^2+ab+b^2\right)+\left(a-b\right)^2\)
\(\left(a-b\right)\left(a^2+ab+b^2+a-b\right)\)
b) \(\left(8a^3-27b^3\right)-2a\left(4a^2-9b^2\right)\)
\(=\left(2a-3b\right)\left(4a^2+6ab+9b^2\right)-2a\left(2a-3b\right)\left(2a+3b\right)\)
\(=\left(2a-3b\right)\left(4a^2+6ab+9b^2-4a^2-6ab\right)\)
\(=\left(2a-3b\right)\cdot9b^2\)
\(=\left(a-b\right)\left(a^2+ab+b^2\right)+a^2-2ab+b^2\)
= ...........
a, \(\left(8a^3-27b^3\right)-2a\left(4a^2-9b^2\right)\)
\(=\left(2a-3b\right)\left[\left(2a\right)^2+2a.3b+\left(3b\right)^2\right]-2a\left(2a-3b\right)\left(2a+3b\right)\)
\(=\left(2a-3b\right)\left[4a^2+6ab+9b^2-2a\left(2a+3b\right)\right]\)
\(=\left(2a-3b\right)\left(4a^2+6ab+9b^2-4a^2-6ab\right)\)
\(=\left(2a-3b\right).9b^2\)
b, \(\left(x^3-y^3\right)+\left(x-y\right)^2\)
\(=\left(x-y\right)\left(x^2+xy+y^2\right)+\left(x-y\right)^2\)
\(=\left(x-y\right)\left[\left(x^2+xy+y^2\right)+\left(x-y\right)\right]\)
\(=\left(x-y\right)\left(x^2+xy+y^2+x-y\right)\)
c, \(\left(m^3+n^3\right)+\left(m+n\right)^2\)
\(=\left(m+n\right)\left(m^2-mn+n^2\right)+\left(m+n\right)^2\)
\(=\left(m+n\right)\left(m^2-mn+n^2+m+n\right)\)
Chúc bạn học tốt!!!