解決{l}{(3x+2y)^3-(2x+y)^3}{27m^6-343n^12} |Microsoft數學求解器

$$\left. \begin{array} { l } { ( 3 x + 2 y ) ^ { 3 } - ( 2 x + y ) ^ { 3 } } \\ { 27 m ^ { 6 } - 343 n ^ { 12 } } \end{array} \right.$$

最小公倍式

$$-\left(x+y\right)\left(3m^{2}-7n^{4}\right)\left(931x^{2}n^{8}+171x^{2}m^{4}+1127xyn^{8}+483xym^{2}n^{4}+207xym^{4}+343y^{2}n^{8}+63y^{2}m^{4}+147n^{4}\left(my\right)^{2}+399n^{4}\left(mx\right)^{2}\right)$$

解題步驟

識別所有運算式的所有因數與其最高乘冪。將這些因數的最高乘冪相乘以取得最小公倍數。

$$\left(x+y\right)\left(3m^{2}-7n^{4}\right)\left(-931x^{2}n^{8}-399m^{2}x^{2}n^{4}-171x^{2}m^{4}-1127xyn^{8}-483xym^{2}n^{4}-207xym^{4}-343y^{2}n^{8}-147m^{2}y^{2}n^{4}-63y^{2}m^{4}\right)$$

展開運算式。

$$6517x^{3}n^{12}-513x^{3}m^{6}+10290xy^{2}n^{12}-810xy^{2}m^{6}+2401y^{3}n^{12}-189y^{3}m^{6}+14406yx^{2}n^{12}-1134yx^{2}m^{6}$$

評估

$$\left(x+y\right)\left(19x^{2}+23xy+7y^{2}\right),\ 27m^{6}-343n^{12}$$