Lời giải :
a) \(VP=\left(a+b\right)\left[\left(a-b\right)^2+ab\right]\)
\(=\left(a+b\right)\left(a^2-2ab+b^2+ab\right)\)
\(=\left(a+b\right)\left(a^2-ab+b^2\right)\)
\(=a^3+b^3=VT\)( đpcm )
b) \(VT=\left(a^2+b^2\right)\left(c^2+d^2\right)\)
\(=a^2c^2+a^2d^2+b^2c^2+b^2d^2\)
\(=a^2c^2+2abcd+b^2d^2+a^2d^2-2abcd+b^2c^2\)
\(=\left(ac+bd\right)^2+\left(ad-bc\right)^2=VP\)( đpcm )
a)CM \(a^3+b^3=\left(a+b\right)\left[\left(a-b\right)^2+ab\right]\)
VT = \(a^3+b^3=\left(a+b\right)\left(a^2-ab+b^2\right)\)
VP = \(\left(a+b\right)\left[\left(a-b\right)^2+ab\right]=\left(a+b\right)\left(a^2-2ab+b^2+ab\right)=\left(a+b\right)\left(a^2-ab+b^2\right)\)
Ta thấy VP = VT
=> \(a^3+b^3=\left(a+b\right)\left[\left(a-b\right)^2+ab\right]\)
b) CM \(\left(a^2+b^2\right)\left(c^2+d^2\right)=\left(ac+bd\right)^2+\left(ad-bc\right)^2\)
VT = \(\left(a^2+b^2\right)\left(c^2+d^2\right)=a^2c^2+a^2d^2+b^2c^2+b^2d^2\)
VP = \(\left(ac+bd\right)^2+\left(ad-bc\right)^2=ac^2+2acbd+bd^2+ad^2-2abcd+bc^2=ac^2+ad^2+bd^2+bc^2\)Ta thấy VP = VT
=> \(\left(a^2+b^2\right)\left(c^2+d^2\right)=\left(ac+bd\right)^2+\left(ad-bc\right)^2\)
