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The distributive property is a key concept in algebra that allows you to simplify expressions by distributing a multiplier across terms within parentheses. In simpler terms, when you have an expression like $$a(b + c),$$ you can rewrite it as $$a \times b + a \times c$$. This helps eliminate the parentheses and makes the equation easier to manage.

Let's break down the example given in the exercise: $$4 + 6(y - 3)$$.
We apply the distributive property by multiplying 6 by each term inside the parentheses (y and -3):

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• $$6 \times y = 6y$$
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• $$6 \times (-3) = -18$$

Putting it all together, the expression becomes $$4 + 6y - 18$$.
This step ensures the parentheses are removed, making it easier to move on to the next steps.

After using the distributive property, the next step in simplifying an algebraic expression is to combine like terms. Like terms are terms that have the same variables raised to the same power. Only the coefficients (numbers in front of the variables) differ.
In the expression $$4 + 6y - 18$$, we see that:

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• The terms $$4$$ and $$-18$$ are constants. They don’t have any variables.
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• The term $$6y$$ has the variable y.

To combine the like terms, we group them together. Constant terms $$4$$ and $$-18$$ can be combined as follows:

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• $$4 - 18 = -14$$

So, the expression now becomes $$6y - 14$$.
This step simplifies the equation further by reducing the number of terms and making it easier to understand.

Constants are the numbers in an algebraic expression that do not change. They don't have variables attached to them. In the example from the exercise, the constants are 4 and -18.

Constants play a significant role in algebraic expressions because they provide fixed values to work with. When simplifying algebraic expressions, combining constants correctly is essential for obtaining the correct answer.

In the expression $$4 + 6(y - 3)$$, after applying the distributive property, we get the constants $$4$$ and $$-18,$$ which we then combine to simplify the expression:

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• $$4 - 18 = -14$$

The presence of constants in an equation makes it possible to simplify it to its most basic form, $$6y - 14$$ in this case, enhancing comprehension and ease of calculation.