Find the Product x(x+3)
The problem is asking you to calculate the result of multiplying two binomial expressions, with the first expression being "x" and the second expression being "x+3". In order to solve this, you would apply the distributive property, also known as the FOIL method for binomials, to find the product of these two expressions. This will involve multiplying each term in the first binomial by each term in the second binomial and combining like terms if necessary to arrive at the final simplified expression.
$x \left(\right. x + 3 \left.\right)$
Answer
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:
We distribute $x$ across the terms inside the parenthesis, which are $x$ and $3$.
We multiply $x$ by $x$ to get $x^2$.
We multiply $x$ by $3$ to get $3x$.
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 $ax^2 + bx + c$, where $a$, $b$, and $c$ are constants, and $a \neq 0$.
