Find the Product x(x+3)

Solution:

Step 1:

Utilize the distributive property to expand the expression: $x\times x+x\times 3$

Step 2:

Proceed to simplify the expanded expression.

Step 2.1:

Calculate the product of $x$ with itself: $x^2+x\times 3$

Step 2.2:

Rearrange the terms to place the constant factor before the variable: $x^2+3x$

Knowledge Notes:

The problem at hand involves finding the product of a binomial, $x(x+3)$. This process requires an understanding of the distributive property, which is a fundamental principle in algebra. The distributive property states that for any three numbers, a, b, and c, the following equation holds true: $a(b+c)=ab+ac$. This property allows us to multiply a single term by each term inside a parenthesis.

In the given problem, we apply the distributive property as follows:

1. We distribute $x$ across the terms inside the parenthesis, which are $x$ and $3$.

2. We multiply $x$ by $x$ to get $x^2$.

3. We multiply $x$ by $3$ to get $3x$.

4. We then combine these two products to obtain the simplified expression $x^2+3x$.

It is important to note that in Step 2.2, the rearrangement of terms is not necessary for the simplification process, as $x\times 3$ is already simplified to $3x$. However, it is a common convention to write terms in descending order of their powers, which is why $x^2$ is written before $3x$.

The final result is a quadratic expression, which is a polynomial of degree 2. Quadratic expressions are commonly found in various mathematical problems and have the general form $a{x}^2+bx+c$, where $a$, $b$, and $c$ are constants, and $a\ne 0$.