Final: The Big Tidy

To simplify a sum of two products, expand each product on its own first. Each product of two binomials gives four terms. Then collect the like terms from both expansions together.

For $\left(x+1\right)\left(x+2\right)+\left(x+3\right)\left(x+4\right)$: the first product expands to $x^{2}+3x+2$, and the second expands to $x^{2}+7x+12$. Adding them and collecting like terms gives $2x^{2}+10x+14$.