Simplify the expression $f\left(x\right)=\left(x+1\right)\left(x-2\right)$

 Main Topic: Product of Binomials with Common Term

In special products, the product of two binomials that have a common term results in a trinomial, whose first term is the square of the common term, the second term is the product of the algebraic sum of the uncommon terms by the common term, and the third term is equal to the product of the uncommon terms. In other words: $(x+a)(x+b)=x^2+(a+b)x+ab$.