Expanding the left side yields 3a square + 3b square + 3c square – 2ab – 2bc – 2ca, which does not match the right side. Therefore, the given mathematical equation is false.
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We substitute a = 3x, b = -2y and c = 4z into the expansion formula. Squaring terms makes them positive, while the cross-products involving the negative y term become negative.
We expand this by substituting a = p, b = 3q and c = 7r into the identity. Squaring the individual items and finding their paired double products yields the answer.
The merchant gets 15 ingots for every 2 spice bags. To find the total for 12 bags, divide 12 by 2 to get 6 pairs, then multiply 6 by 15, resulting in 90 copper ingots.
The equation is w = 3d. For a distance of d = 2 units, substituting it into the linear equation gives the work done as w = 3(2) = 6 units. Plotting (2, 6) confirms this on the graph.