Problem 80 - Algebra 1: Concepts and Skills

Question

Find the product. $$(6 x+2)\left(x^{2}-x-1\right)$$

Step-by-Step Solution

Answer

The solution to the given problem is \( 6x^{3} -4x^{2} -8x -2 \)

Step 1: Application of the Distributive Property

Commence with applying the distributive property. Multiply each term in the binomial with all the terms in the trinomial: \( (6x \cdot x^{2})+(6x \cdot -x)+(6x \cdot -1)+(2\cdot x^{2})+(2 \cdot -x)+(2\cdot -1) \)

Step 2: Simplify

Now, multiply the constants: \(6x^{3} -6x^{2} -6x +2x^{2} -2x -2 \)

Step 3: Combine like terms

Combine like terms to simplify the expression further: \( 6x^{3} +(2x^{2}-6x^{2})+(-6x-2x)+(-2) = 6x^{3} -4x^{2} -8x -2 \)