### Simplifying Variable Expressions Worksheets

Simplifying variable expression is basically combining like terms and/or using the distributive property. Hence, signs of grouping such as parentheses ( ), brackets [ ], and braces { } may present in simplifying algebraic expressions. The word parentheses, which will refer to any of these symbols, are used to enclose terms whose sum is to act as a single number.

Using the distributive property, i.e. $$a(b+c)=ab+ac$$ for all real numbers a, b, and c, a factor multiplying a sum within parentheses should be used to multiply each term of the sum.

Examples:

1. $$-2(2a-2b+3) = -2(2a)-2(-2b)-2(3) = -4a+4b-6$$
2. $$3(a+c) = 3(a)+3(c) = 3a+3c$$

A sign "+" or "-" before an algebraic expression indicates multiplication by $$+1$$ or $$-1$$, respectively. Thus, to remove or insert parentheses preceded by a plus sign, we just rewrite the included terms unchanged. If it is preceded by minus sign, we just rewrite the included terms with their signs changed.

Examples:

1. $$+(a+2b-3c)=a+2b-3c$$
2. $$-(3a-4b)=(-1)(3a-4b)=-3a+4b$$
3. $$-[3x-(y+3+z)]=-(3x-y-3-3z)=-3x+y+3z+3$$

Two terms with the same literal part are called similar terms regardless of their coefficients, the numerical parts of the terms. If similar terms occur in an algebraic expression and there is no need to apply distributive property, these terms can be added or subtracted by adding or subtracting their numerical coefficients and multiply the result by the common literal part.

Examples:

1. $$-3x+17x=(-3+17)x=14x$$
2. $$(2x-3y-2)-(3x+5y-10)=2x-3y-2-3x-5y+10=-x-8y+8$$

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