The expression representing the product of $4$ and $y$ is denoted as $4y$.

In mathematics, the term “product” refers to the result obtained from multiplying two or more numbers. Specifically, when we discuss the product of $4$ and $y$, we are essentially multiplying the number $4$ by the variable $y$. This relationship can be succinctly expressed as $4y$, where $4$ serves as the coefficient and $y$ is the variable.

In algebra, it is customary to write the coefficient (the numerical part) directly adjacent to the variable without including a multiplication sign. Therefore, instead of writing $4 * y$, we simply write $4y$. This notation is more streamlined and is commonly employed in mathematical expressions and equations.

Grasping how to create and manipulate such expressions is vital in GCSE Maths, as it lays the groundwork for tackling more intricate algebraic problems. For instance, if you know the value of $y$, you can readily determine the value of $4y$ by substituting $y$ with its specific value and carrying out the multiplication. If $y$ equals $3$, then $4y$ would be calculated as $4 * 3$, which equals $12$.

This concept also applies to solving equations. For example, if you encounter an equation like $4y = 20$, you can isolate $y$ by dividing both sides of the equation by $4$. This process yields $y = 5$. Developing a fundamental understanding of algebraic expressions and equations is essential for advancing in mathematics.