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When you first look at an algebraic expression like \(2(x+1)+20\), distributing can make it easier to manage. The distributive property is a fundamental algebraic rule that allows you to multiply a single term by each term inside the parentheses. This helps to eliminate the parentheses.

Imagine you have two groups within the parentheses: \(x + 1\). You need to multiply each group by 2, which is outside. This is like sharing equally to each member inside the brackets:

• Distribute 2 to \(x\) to get \(2 \times x\), which is \(2x\).
• Next, distribute 2 to 1, and you'll get \(2 \times 1\), which is 2.

After distributing, the expression \(2(x+1)+20\) becomes \(2x + 2 + 20\). Distributing can seem like a simple step, but it's crucial because it breaks down expressions and helps with further breakdowns and simplifications.

Once you've used the distributive property, the next step is to simplify your expression by combining like terms.

What are like terms? In algebra, like terms are terms that have the same variable raised to the same power. When simplifying expressions, combining these terms can significantly reduce the complexity of your work.

• Take note: You can only combine constants with constants and variables with the same variables.
• In the expression \(2x + 2 + 20\), the numbers 2 and 20 are constants because they don't have variables attached to them.

So we add the constants 2 and 20 to get 22, making the expression \(2x + 22\).

Remember, combining like terms helps you to neatly simplify your algebraic expressions, making long equations much easier to handle.

An algebraic expression is a combination of variables, numbers and at least one operation (such as addition, subtraction, multiplication, or division). They do not have an equal sign, but they can be simplified or factored using various algebraic rules.

Algebraic expressions like \(2(x+1)+20\) can initially look a bit intimidating because of the mixture of numbers and letters. But remember:

• Each number or letter is a term. Letters like \(x\) are variables that can represent any number.
• Numeric terms, like 20 in this example, are constants because their values never change.
• Operations like addition and multiplication help connect these terms in meaningful ways.

By applying properties such as the distributive property and combining like terms, you can transform complex algebraic expressions into simpler and more manageable forms. This simplification allows you to solve for variables or prepare for more advanced computations.