Expand the product ${(x+2)(x+5)}$.
To expand a product of two binomials, I can use the distributive property. I can write ${(x+2)(x+5)}$ as ${x(x+5) + 2(x+5)}$ and then apply the distributive property to each term. For the first term, ${x(x+5)}$, I can multiply x by each term in the parentheses and get ${x^2 + 5x}$. For the second term, ${2(x+5)}$, I can multiply 2 by each term in the parentheses and get ${2x + 10}$. Now I can add the two terms together and simplify. I get ${x^2 + 5x + 2x + 10}$. Combining like terms, I get ${x^2 + 7x + 10}$. 