\(B8:\)\(M=a^3+b^3+3ab\left(a^2+b^2\right)+6a^2b^2\left(a+b\right)\)
\(=\left(a+b\right)^3-3ab\left(a+b\right)+3ab\left(a^2+b^2\right)+6a^2b^2\)
\(=1-3ab\left(1-a^2-b^2\right)+6.\left(ab\right)^2\)
\(=1-3ab\left[1-\left(a^2+2ab+b^2-2ab\right)\right]+6\left(ab\right)^2\)
\(=1-3ab\left[1-\left(1-2ab\right)\right]+6\left(ab\right)^2=1-3ab\left(2ab\right)+6\left(ab\right)^2=1-6\left(ab\right)^2+6\left(ab\right)^2=1\)
\(B7:ax+by+cz=0\Rightarrow\left(ax+by+cx\right)^2=0\)
\(\Leftrightarrow\left(ax\right)^2+\left(by\right)^2+\left(cz\right)^2+2\left(axzc+axby+bycz\right)=0\)
\(\Rightarrow-2\left(axzc+axby+bycz\right)=\left(ax\right)^2+\left(by\right)^2+\left(cz\right)^2\)
\(A=\dfrac{bc\left(y-z\right)^2+ca\left(z-x\right)^2+ab\left(x-y\right)^2}{ax^2+by^2+cz^2}=\dfrac{abx^2+aby^2+bcy^2+bcz^2+caz^2+cax^2+\left(ax\right)^2+\left(by\right)^2+\left(cz\right)^2}{ax^2+by^2+cz^2}=\dfrac{\left(a+b+c\right)\left(ax^2+by^2+cz^2\right)}{ax^2+by^{^2}+cz^2}=a+b+c\)
Bài 8:
\(M=\left(a+b\right)^3-3ab\left(a+b\right)+3ab\left[\left(a+b\right)^2-2ab\right]+6a^2b^2\cdot1\)
\(=1^3-3ab+3ab\cdot1-3ab\cdot2ab+6a^2b^2=1\)
