Simplify x(27-x)(18-2x)

Problem

x*(27−x)*(18−2*x)

Solution

1. Factor out the common factor of 2 from the third term (18−2*x) to simplify the expression.

x*(27−x)⋅2*(9−x)

2*x*(27−x)*(9−x)

2. Expand the product of the two binomials (27−x) and (9−x) using the FOIL method.

(27⋅9)+(27⋅−x)+(−x⋅9)+(−x⋅−x)

243−27*x−9*x+x2

3. Combine the like terms inside the parentheses.

x2−36*x+243

4. Distribute the remaining 2*x across the trinomial.

2*x(x2)+2*x*(−36*x)+2*x(243)

2*x3−72*x2+486*x

Final Answer

x*(27−x)*(18−2*x)=2*x3−72*x2+486*x

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