Simplifying a rational expression by factoring

The video tutorial explains how to handle mathematical expressions with terms separated by addition or subtraction, emphasizing the common mistake of misapplying exponent rules. It introduces the concept of rewriting expressions as multiplication through factoring, covering techniques like finding the greatest common factor (GCF) and the difference of squares. The tutorial also demonstrates factoring trinomials using the box method and concludes with simplifying expressions by dividing out common terms.

Why can't you apply the rules of exponents directly to terms separated by addition or subtraction?

• Because they have different coefficients.

• Because they are not in the same order.

• Because they are not like terms.

• Because they are separated by operations other than multiplication.

What is the first step in rewriting an expression as multiplication?

• Factoring out the greatest common factor.

• Applying the rules of exponents.

• Combining like terms.

• Simplifying the coefficients.

What is the factored form of the expression X^2 - 4?

• (X - 2)(X + 2)

• (X - 3)(X + 3)

• (X - 4)(X + 4)

• (X - 1)(X + 1)

When factoring trinomials, what do you look for in the numbers?

• Numbers that are both even.

• Numbers that are both prime.

• Numbers that multiply to give the constant term and add to give the middle term.

• Numbers that are both odd.

How can you simplify an expression once it is in factored form?

• By dividing all the terms by the same number.

• By canceling out common terms in the numerator and denominator.

• By multiplying all the terms together.

• By adding all the terms together.