Question

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

Short answer

The product of \((6x+2)(x^{2}-x-1)\) is \(6x^{3}-4x^{2}-8x-2\)

Step-by-step solution

Distribute First Term

First, distribute the first term of the binomial \(6x\) to each term in the trinomial: \(6x*x^{2}\), \(6x*-x\), and \(6x*-1\). This gives: \(6x^{3}-6x^{2}-6x.\)

Distribute Second Term

Next, distribute the second term of the binomial \(2\) to each term in the trinomial: \(2*x^{2}\), \(2*-x\), and \(2*-1\). This gives: \(2x^{2}-2x-2.\)

Combine like terms

The final step is to add the two results together. Combine the terms from Step 1 and Step 2 to get the final result. This yields: \(6x^{3}-6x^{2}-6x+2x^{2}-2x-2 = 6x^{3}-4x^{2}-8x-2.\)