Problem 81 - Algebra 1: Concepts and Skills

Question

Find the product. $$(2 x-1)\left(x^{2}+x+1\right)$$

Step-by-Step Solution

Answer

The product of \((2x-1)\) and \((x^2+x+1)\) is \(2x^3 + x^2 + x - 1\).

Step 1: Distribute the first term of the binomial

Distribute \(2x\) to each term in the trinomial. This results in: \(2x(x^2) + 2x(x) + 2x(1)\) which simplifies to \(2x^3+2x^2+2x\).

Step 2: Distribute the second term of the binomial

Now distribute \(-1\) (the second term of the binomial) to each term of the trinomial. This gives \(-1(x^2) - 1(x) - 1(1)\) which simplifies to \(-x^2 - x -1\).

Step 3: Add like terms

Add together the results of the distributions to combine like terms: \((2x^3+2x^2+2x) + (-x^2 - x -1)\). This simplifies to \(2x^3 + x^2 + x - 1\).