Factor out the greatest common factor from each expression....

Key Concepts

Distributive Property

The distributive property allows one to factor or expand expressions by multiplying a single term by each term within parentheses. When factoring, the process is essentially the reverse of distribution: extracting the common factor from each term so that the expression is written as a product of the gcd and another simpler expression.

Exponent Rules

Exponent rules are used to manage terms with powers, especially when factoring expressions that include variables raised to fractional or integer exponents. Specifically, when identifying the common variable factors, one uses the rule that the lower exponent common to all terms is the one that can be factored out, leaving the remainder in each term's exponent.

Greatest Common Factor (GCF)

The greatest common factor is the largest expression or number that divides each term of an algebraic expression without leaving a remainder. It involves looking at both the numerical coefficients and the variable parts, selecting the highest factor common to all terms, simplifying the expression in the process.

Factoring

Factoring is the method of rewriting an expression as a product of factors. In algebra, it is often useful to factor an expression by taking out the greatest common factor from each term, which simplifies the expression and can ease further manipulation, such as solving equations or simplifying complex expressions.

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