how do you solve factoring the binomial by grouping (x +3)y = (x+3)6=
To solve factoring the binomial by grouping, let's break down the problem step by step.
First, let's rewrite the expression: (x + 3)y = (x + 3)6
To factor the binomial by grouping, we need to find common factors in both terms on the right side of the equation.
Step 1: Identify the common binomial factor
In this case, the common binomial factor is (x + 3), which appears in both terms on the right side of the equation.
Step 2: Extract the common binomial factor
We can rewrite the equation by extracting the common binomial factor from both terms:
(x + 3)y = 6(x + 3)
Step 3: Remove the parentheses
Now we remove the parentheses by distributing the common binomial factor to both terms:
xy + 3y = 6x + 18
Step 4: Rearrange the equation
We rearrange the equation by bringing all the terms to one side to achieve the standard form:
xy - 6x = 18 - 3y
Step 5: Factor out the common variables
We can further factor the equation by extracting the common variables from both terms:
x(y - 6) = 18 - 3y
This is the factored form of the original equation.
To summarize, to factor the binomial by grouping, follow these steps:
1. Identify the common binomial factor.
2. Extract the common binomial factor.
3. Remove the parentheses by distributing the common binomial factor to both terms.
4. Rearrange the equation to achieve the standard form.
5. Factor out the common variables.
Always make sure to check your factored equation for possible further simplifications or solutions if required.