Simplify (2x-5)(x^2-x+1)

Problem

(2*x−5)*(x2−x+1)

Solution

1. Distribute the first term of the binomial, 2*x to each term in the trinomial.

2*x(x2)+2*x*(−x)+2*x(1)

2*x3−2*x2+2*x

2. Distribute the second term of the binomial, −5 to each term in the trinomial.

−5*(x2)−5*(−x)−5*(1)

−5*x2+5*x−5

3. Combine the results of the distribution into a single expression.

2*x3−2*x2+2*x−5*x2+5*x−5

4. Group and combine the like terms, specifically the x2 terms and the x terms.

2*x3+(−2*x2−5*x2)+(2*x+5*x)−5

2*x3−7*x2+7*x−5

Final Answer

(2*x−5)*(x2−x+1)=2*x3−7*x2+7*x−5

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