ГДЗ по алгебре 7 класс Макарычев ФГОС Задание 1020

\[\boxed{\text{1020.}\text{\ }еуроки - ответы\ на\ пятёрку}\]

\[\left( p^{2} + cq^{2} \right)\left( r^{2} + cs^{2} \right) = p^{2}r^{2} +\]

\[+ cp^{2}s^{2} + cr^{2}q^{2} + c^{2}s^{2}q^{2}\]

\[(pr + cqs)^{2} + c(ps - qr)^{2} =\]

\[= p^{2}r^{2} + 2prcqs + c^{2}q^{2}s^{2} +\]

\[+ c\left( p^{2}s^{2} - 2psqr + q^{2}r^{2} \right) =\]

\[= p^{2}r^{2} + 2prcqs + c^{2}q^{2}s^{2} +\]

\[+ cp^{2}s^{2} - 2psqrc + cq^{2}r^{2} =\]

\[= p^{2}r^{2} + cp^{2}s^{2} + cr^{2}q^{2} +\]

\[+ c^{2}s^{2}q^{2} \Longrightarrow следовательно,\ \]

\[\left( p^{2} + cq^{2} \right)\left( r^{2} + cs^{2} \right) =\]

\[= (pr + cqs)^{2} + c(ps - qr)^{2}\]