Simplify y*y*3
The given question "Simplify y_y_3" is asking for the simplification of a mathematical expression. The expression contains a variable 'y' that is squared (multiplied by itself) and then multiplied by a constant integer '3'. The task is to perform the multiplication and express the product in the simplest form, representing it as an algebraic expression.
$y \cdot y \cdot 3$
Answer
Solution:
Step 1:
Compute the product of $y$ with itself, which is $y \times y = y^2$. Then, you have $y^2 \cdot 3$.
Step 2:
Rearrange the expression to place the constant before the variable, resulting in $3y^2$.
Knowledge Notes:
To simplify an expression like $y \cdot y \cdot 3$, we need to understand the following concepts:
Multiplication of Variables: When you multiply a variable by itself, you are essentially raising it to a power. The expression $y \cdot y$ is the same as $y^2$. This is due to the exponent rule that states when multiplying like bases, you add the exponents. Since $y$ is the same as $y^1$, multiplying it by itself ($y^1 \cdot y^1$) gives you $y^{1+1}$, which simplifies to $y^2$.
Commutative Property of Multiplication: This property states that you can change the order of the factors in a multiplication problem without changing the product. For example, $3 \cdot y^2$ is the same as $y^2 \cdot 3$. We often rearrange terms to place constants before variables for a more standardized form, which can make it easier to read and further manipulate algebraically.
Simplification: Simplifying an expression means to make it as concise and straightforward as possible. In algebra, this often involves combining like terms, rearranging terms for clarity, and reducing expressions to their simplest form.
By applying these concepts, we can simplify the given expression $y \cdot y \cdot 3$ to $3y^2$.
