Simplify the following expression: 21(x-4)+2
The Correct Answer and Explanation is:
Correct Answer:
21(x−4)+2=21x−8221(x – 4) + 2 = 21x – 8221(x−4)+2=21x−82
Explanation
To simplify the algebraic expression 21(x−4)+221(x – 4) + 221(x−4)+2, we need to apply the distributive property and then combine like terms. The distributive property allows us to multiply a number outside the parentheses by each term inside the parentheses.
Here is the step-by-step process:
- Distribute the 21 across the terms inside the parentheses: 21(x−4)=21⋅x−21⋅4=21x−8421(x – 4) = 21 \cdot x – 21 \cdot 4 = 21x – 8421(x−4)=21⋅x−21⋅4=21x−84
- Add the constant outside the parentheses (which is +2) to the expression obtained from the distribution: 21x−84+221x – 84 + 221x−84+2
- Combine like terms. Here, the like terms are the constants −84-84−84 and +2+2+2. When we combine them: −84+2=−82-84 + 2 = -82−84+2=−82
- Write the final simplified expression: 21x−8221x – 8221x−82
This simplified form of the expression 21(x−4)+221(x – 4) + 221(x−4)+2 is in the standard linear form ax+bax + bax+b, where a=21a = 21a=21 and b=−82b = -82b=−82.
Understanding how to simplify expressions is important in algebra because it makes equations easier to work with, especially when solving or graphing. Distributing and combining like terms are foundational algebraic skills. They are used in solving equations, factoring, and even in calculus later on. In this case, you see how a multi-step expression simplifies into a cleaner and more usable format.
Remember that the parentheses indicate multiplication, and any number added or subtracted outside the parentheses should only be combined after distributing first. Always follow the order of operations: distribution (multiplication), then addition or subtraction.
