Đặt
\(\dfrac{a}{b}=\dfrac{c}{d}=k\) \(\Rightarrow\left\{{}\begin{matrix}a=bk\\c=dk\end{matrix}\right.\)
\(\Rightarrow\left(a+2c\right)\left(b+d\right)=\left(bk+2dk\right)\left(b+d\right)\)
\(=bk\left(b+d\right)+2dk\left(b+d\right)\)
\(=b^2k+bdk+2bdk+2d^2k\)
\(=b^2k+3bdk+2d^2k\)
\(\Rightarrow\left(a+c\right)\left(b+2d\right)=\left(bk+dk\right)\left(b+2d\right)\)
\(=bk\left(b+2d\right)+dk\left(b+2d\right)\)
\(=b^2k+2bdk+bdk+2d^2k\)
\(=b^2k+3bdk+2d^2k\)
\(VT=VP\)\(\Rightarrowđpcm\)
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