How does 3x(4x+5)-5(4x+5) factor out to be (4x+5)(3x-5) ? This may be wrong, because I wrote this answer in my notes, but could some one please explain this to me? Also, do you have any tips on factoring? I understand the concept when I see an example(Usually), but I have a very hard time actually doing it.
You have two different terms (3x and -5) that both multiply (4x + 5) . You can add these two terms together into (3x - 5)
You are using the "distributive" rule that
(x + y)z = xz + yz
but in this case you are using it "backwards".
x, y and z can be constants or algebraic terms
To factor the expression 3x(4x+5)-5(4x+5), you can use a common factor technique. The key idea is to look for common factors between the terms and factor them out.
Step 1: Observe that both terms have a factor of (4x+5). Rewrite the expression to highlight this common factor:
(4x+5)(3x) - (4x+5)(5)
Step 2: Notice that the common factor (4x+5) appears in both terms. We can now factor it out:
(4x+5)[3x - 5]
By factoring out the common factor, we simplify the expression and arrive at the factored form (4x+5)(3x-5).
As for tips on factoring, here are a few strategies that may help:
1. Look for common factors between terms: In many cases, expressions contain common factors between terms. By identifying and factoring out these common factors, you can simplify the expression.
2. Use the distributive property: The distributive property allows you to distribute a factor to each term within parentheses. This can help simplify expressions and facilitate factoring.
3. Factor by grouping: Sometimes, you may need to group terms together in order to factor. Look for patterns or similarities among the terms and group them accordingly. Then, factor out common factors within each group.
4. Practice, practice, practice: Factoring often becomes easier with practice. The more you practice factoring different types of expressions, the more familiar you will become with the patterns and techniques involved.
Remember that factoring can sometimes be challenging, and it may take time to develop proficiency. Keep practicing, seek additional examples or resources, and don't hesitate to ask for help when needed.