An algebraic expression has parentheses with unlike terms inside. Explain how to simplify this algebraic expression if a minus sign is in front of the parentheses.

If you have an algebraic expression with parentheses containing unlike terms, and there's a minus sign in front of the parentheses, you can use the distributive property to simplify the expression. The distributive property states that for any real numbers �

a, �

b, and �

c:

�⋅(�−�)=�⋅�−�⋅�

a⋅(b−c)=a⋅b−a⋅c

So, when you have a minus sign in front of the parentheses, you can distribute the minus sign to each term inside the parentheses. Here's the step-by-step process:

1.Distribute the minus sign to each term inside the parentheses.

2.Combine like terms.

Let's go through an example to illustrate the process. Consider the expression:

−2⋅(3�−4�+2)

−2⋅(3x−4y+2)

Step 1: Distribute the minus sign to each term inside the parentheses:

−2⋅3�+(−2)⋅(−4�)+(−2)⋅2

−2⋅3x+(−2)⋅(−4y)+(−2)⋅2

This gives:

−6�+8�−4

−6x+8y−4

Step 2: Combine like terms if possible. In this case, there are no like terms to combine, so the expression is already simplified:

−6�+8�−4

−6x+8y−4

So, the simplified form of the expression −2⋅(3�−4�+2)

−2⋅(3x−4y+2) is −6�+8�−4

−6x+8y−4.