What is the difference between expanding and factoring

Removing brackets from an expression is known as expanding the expression. This usually occurs when a term outside a bracket is multiplied by every term inside the bracket. The outside term "distributes" itself over the inside terms. Thus the name the distributive property.

Difference Between Expanding and Factoring. Difference Between Similar Terms and Objects. MLA 8 Franscisco,. Name required. Email required. Please note: comment moderation is enabled and may delay your comment. There is no need to resubmit your comment. Notify me of followup comments via e-mail. Written by : Celine. User assumes all risk of use, damage, or injury. You agree that we have no liability for any damages. Summary: 1. Group 5: Trinomials.

Group 6: General Trinomials. General Factoring Strategy Check for common factors. If the terms have common factors, then factor out the greatest common factor GCF and look at the resulting polynomial factors to factor further. Determine the number of terms in the polynomial. Look for factors that can be factored further. Check by multiplying.

Factoring called "Factorising" in the UK is the process of finding the factors: Factoring: Finding what to multiply together to get an expression. It is like "splitting" an expression into a multiplication of simpler expressions. Note: Different pairing of terms may or may not lead to a useful factorisation. Factoring can give us useful information regarding an expression as the following exercise shows.

There are three special expansions and corresponding factorisations that frequently occur in algebra. The first of these is an identity known as the difference of squares. An identity is a statement in algebra that is true for all values of the pronumerals.

Hence the difference between the squares of two numbers equals their sum times their difference. One such application is to mental arithmetic. With practice this can be done mentally, provided the squares of integers up to about 20 are known.

The difference of two squares can also be used to solve equations in which we only seek integer solutions. These identities are harder to use than the difference of two squares and are probably best dealt with as special cases of quadratic factoring, discussed below. The following example shows how these ideas can be cleverly combined to factor an expression that at first glance does not appear to factor.

At first glance this expression does not appear to factor, since there is no identity for the sum of squares. However, by adding and subtracting the term , we arrive at a difference of squares. This expansion produces a simple quadratic. We would like to find a procedure that reverses this process.

We notice that the coefficient x of is the sum of the two numbers 2 and 5 in the brackets and that the constant term 10, is the product of 2 and 5. This suggests a method of factoring. Hence to reverse the process, we seek two numbers whose sum is the coefficient of and whose produce is the constant term.

Clearly the solutions are 4 and 3 in either order , and no other numbers satisfy these equations. Students should try to mentally expand to check that their answers are correct. Also note that the difference of squares factorisation could also be done using this method.

This is, however, not a good method to use. It is better for students to be on the look out for the difference of squares identity and apply it directly.