Algebraic Expressions - Trivium Test Prep Online Courses

Algebraic Expressions

Algebraic Expressions

Evaluating Expressions

The foundation of algebra is the variable, an unknown number represented by a symbol (usually a letter such as x or a). Variables can be preceded by a coefficient, which is a constant in front of the variable, such as 4x or −2a

An algebraic expression is any sum, difference, product, or quotient of variables and numbers (such as 2x + 7y − 1). The value of an expression is found by replacing the variable with a given value and simplifying the result.

Find the value of x 2 + 3 when x = 5.

x 2 + 3

(5)2 + 3 = 28

Adding and Subtracting Expressions

Terms are any quantities that are added or subtracted in an expression. For example, the terms of the expression x2 + 5 are x2 and 5. Like terms are terms with the same variable part. For example, in the expression 2x + 3xy – 2z + 6y + 2xy, the like terms are 3xy and 2xy.

Expressions can be added or subtracted by simply adding and subtracting like terms. The other terms in the expression will not change.

2x + 3xy – 2z + 6y + 2xy 2x – 2z + 6y + (3xy + 2xy) 2x – 2z + 6y + 5xy

Distributing and Factoring

Simplifying expressions may require distributing and factoring, which are opposite processes.

To distribute, multiply the term outside the parentheses by each term inside the parentheses. For each term, coefficients are multiplied, and exponents are added (following the rules of exponents).

2x (3x 2 + 7) = 6x 3 + 14x

Factoring is the reverse process: taking a polynomial and writing it as a product of two or more factors. The first step in factoring a polynomial is always to “undistribute,” or factor out, the greatest common factor (GCF) among the terms. The remaining terms are placed in parentheses

14a 2 + 7a = 7a(2a + 1)

You can check your factoring by redistributing the term outside the parentheses.

To multiply binomials (expressions with two terms), use FOIL: First – Outer – Inner – Last. Multiple the first term in each expression, the outer terms, the inner terms, and the last term in each expression. Then simplify the expression.

(2x + 3)(x – 4) 

= (2x)(x) + (2x)( –4) + (3)(x) + 3(–4) 

= 2x2 – 8x + 3x –12 

=  2x2 – 5x – 12

When variables occur in both the numerator and the denominator of a fraction, they cancel each other out. So, a fraction with variables in its simplest form will not have the same variable on the top and bottom.

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