1) \(\left(y+3\right)^3-\left(y-1\right)^3\)
=(y+3-y+1)\(\left[\left(y+3\right)^2+\left(y+3\right)\left(y-1\right)+\left(y-1\right)^2\right]\)
=4.(\(y^2+6y+9\)+\(y^2-y+3y-3\)+\(y^2-2y+1\))
=4(\(3y^2+6y+7\))
=\(12y^2+24y+28\)
3.
\(a^3+b^3=\left(a+b\right).\left(a^2-ab+b^2\right)\)
\(=1.\left(a^2+b^2-ab\right)\) (1)
Lại có : \(a^2+b^2=\left(a+b\right)^2-2ab=1-2ab\) thay vào (1) có :
\(a^3+b^3=1.\left(1-2ab-ab\right)\)
\(=1-3ab\left(đpcm\right)\)
2.
\(A=\left(m+n\right)^3+2m^2+4mn+2n^2\)
\(=\left(m+n\right)^3+\left(\sqrt{2}m\right)^2+2.\sqrt{2}m.\sqrt{2}n+\left(\sqrt{2}n\right)^2\)
\(=\left(m+n\right)^3+\left(\sqrt{2}m+\sqrt{2}n\right)^2\)
\(=7^3+\left(\sqrt{2}.7\right)^2=343+98=441\)
( Do \(m+n=7\) )
a) y3+3.y2.3+3.y.32+33=y3+9y2+27y+9
