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Expand the following: (a+b-c)3.

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6. Expand the following: (a+b−c)3(a+b-c)^3.

Step 1: Group terms and apply the binomial expansion (X−Y)3=X3−3X2Y+3XY2−Y3(X-Y)^3 = X^3 - 3X^2Y + 3XY^2 - Y^3.
Let X=(a+b)X = (a+b) and Y=cY = c.

(a+b−c)3=((a+b)−c)3(a+b-c)^3 = ((a+b)-c)^3 =(a+b)3−3(a+b)2c+3(a+b)c2−c3= (a+b)^3 - 3(a+b)^2c + 3(a+b)c^2 - c^3

Step 2: Expand (a+b)3(a+b)^3 and (a+b)2(a+b)^2.

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