#160; #160;2m #160;+ #160;3n3 #160; #160;3m #160;+ #160;2n3=2m #160;+ #160;3n #160; 3m #160;+ #160;2n #160;2m #160;+ #160;3n2 ...

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(x±a)(x±b) = x²±(a+b)x+ab.

2 m+3 n3-3 m+...

Question

(2m + 3n)³ $-$ (3m + 2n)³

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Solution

${(2 m + 3 n)}^{3} - {(3 m + 2 n)}^{3} = [(2 m + 3 n) - (3 m + 2 n)] [{(2 m + 3 n)}^{2} + (2 m + 3 n) (3 m + 2 n) + {(3 m + 2 n)}^{2}] = (- m + n) (4 m^{2} + 12 m n + 9 n^{2} + 6 m^{2} + 4 m n + 9 m n + 6 n^{2} + 9 m^{2} + 12 m n + 4 n^{2}) = (- m + n) (19 m^{2} + 37 m n + 19 n^{2})$

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