Combining like terms, distribution, and factoring

Q: Factor the following expressions using the greatest common factor. 1. -28x+42y-49z 2. 6+42a-30b+6c

A. 1. 7(-4x+6y-7z) 2. 6(1+7a-5b+c)

Q: Factoring is like...? We usually use...?

A: Factoring is like distribution in reverse. We usually use the greatest common factor.

Q: What operation do we use for distribution? Example: 7a^2(4+5a-6u) = ?

A: Multiplication. Don't forget to pay attention to signs!

Q: If you see a plus sign in front of a pair of parentheses, what should you do? If you see a minus sign in front of a pair of parentheses, what should you do? Examples: Rewrite the following expressions without parentheses. (-a+2b)+(3c-4d)=? (-a+2b)-(3c-4d)=? (-a+2b)+(-3c+4d)=? (-a+2b)-(-3c+4d)=?

A: Plug sign: Keep the sign of every term inside (like multiplying by 1). Minus sign: Change the sign of every term inside (like multiplying by -1). Examples solutions: (-a+2b)+(3c-4d)=-a+2b+3c-4d (-a+2b)-(3c-4d)=-a+2b-3c+4d (-a+2b)+(-3c+4d)=-a+2b-3c+4d (-a+2b)-(-3c+4d)=-a+2b+3c-4d

Q: What are like terms?

A: Terms that all have the same variables raised to the same exponents or all do not have any variables.

Q: You MAY NOT use which two operations with unlike terms? However, you MAY use which two operations with unlike terms?

A: You may not add or subtract unlike terms. However, unlike terms may be multiplied or divided.