Two siblings are three years apart
in age. Write an equation for 𝑃, the
product of their ages, in terms of 𝑎, the age of the youngest sibling.
So, we’re told in this question to
use the letter 𝑎 to represent the age of the younger sibling. We now want to find an expression
in terms of 𝑎 for the age of the older sibling. Well, we’re told that the siblings
are three years apart in age. So, the older sibling is three
years older than the younger. An expression for the age of the
older sibling is, therefore, 𝑎 plus three. The product of their ages means we
need to multiply them together. So, we take our two expressions of
𝑎 and 𝑎 plus three and multiply them.
This is a quadratic equation. Because if we were to distribute
the parentheses, we have 𝑎 multiplied by 𝑎 giving 𝑎 squared and 𝑎 multiplied by
three giving three 𝑎. Either of these two forms would be
acceptable for the answer, but we’ll give our answer as 𝑃 equals 𝑎 multiplied by
𝑎 plus three.