Given m ^ 2-MN = 21, Mn-N ^ 2 = - 12, find m ^ 2-N ^ 2, m ^ 2-2mn + n ^ 2 | Math enthusiast | Mathematical art

Given m ^ 2-MN = 21, Mn-N ^ 2 = - 12, find m ^ 2-N ^ 2, m ^ 2-2mn + n ^ 2

solution
m²-mn=21
mn-n²=-12
Two formula addition
m²-mn+mn-n²=21+(-12)=9
∴
m²-n²=9
Subtraction of two formulas
m²-mn-nm+n²=21-(-12)=21+12=33
∴m²-2mn+n²=33

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