Use the distributive property with factoring to find the equivalent expression. 27x + 15y = ? (9x + ? y) Please help! I don’t understand!
The Correct Answer and Explanation is:
To simplify 27x+15y27x + 15y27x+15y using the distributive property with factoring, we want to factor out the greatest common factor (GCF) from the two terms. Here’s a step-by-step explanation:
Step 1: Identify the greatest common factor (GCF)
Look at the coefficients of the terms, which are 27 and 15. The GCF of 27 and 15 is 3 because 3 is the largest number that divides both 27 and 15 evenly.
Step 2: Factor out the GCF
Now, we factor out 3 from each term: 27x+15y=3(9x)+3(5y)27x + 15y = 3(9x) + 3(5y)27x+15y=3(9x)+3(5y)
We can see that each term now has a 3 factored out. The remaining terms inside the parentheses are 9x9x9x and 5y5y5y.
Step 3: Write the equivalent expression
After factoring out the GCF (3), we can now write the expression as: 27x+15y=3(9x+5y)27x + 15y = 3(9x + 5y)27x+15y=3(9x+5y)
So, the equivalent expression is 3(9x+5y)3(9x + 5y)3(9x+5y).
Explanation:
The distributive property states that for any numbers aaa, bbb, and ccc, we have: a(b+c)=ab+aca(b + c) = ab + aca(b+c)=ab+ac
In our case, we factored out the 3, and the distributive property allows us to re-write the expression in factored form as 3(9x+5y)3(9x + 5y)3(9x+5y).
This process is useful because it helps simplify the expression by factoring out common terms, which is often helpful in algebraic manipulations, especially when solving equations or simplifying expressions.
So, the equivalent expression is: 27x+15y=3(9x+5y)27x + 15y = 3(9x + 5y)27x+15y=3(9x+5y)
