This week, we learned how to factorize trinomials. In this blog post, I am going to show you the steps and tricks you can use.

Expanding an equation is finding the answer by multiplying the two monomials together. But what happens when we go backwards? That is called Factoring. 

Let’s say we have an equation that looks like this:

– 32x +48

We need to find the GCF that can be divided into everyone of these terms. In this case, the GCF is 4. Then you will divide each term by four. But if you divide, you also need to multiply the equation by four to cancel it out.

My explanation should look something like this:

4( /4 – 32/4 + 48/4)

Once you have divide each term by their GCF, your answer should look like this:

4( – 8x +12)

What is an exponent? What does it tell you to do?

• The exponent of a number says how many times to use a number in multiplication or how many copies are being made of a number.
• An example is = = 125.
• A common mistake made, is that people assume that =
• We need to remember that the exponent is the number of copies being made of the base and not the multiplication of the two numbers.

Evaluating Exponents. How do brackets affect evaluating a power? 

• Exponents are lazy!
• If you have = (-3)(-3) = 9

In this case, the exponent 2 sees the negative three in the brackets and copies the whole equation twice.

• However, if you have the equation , the exponent will only copy the 3 (not the negative sign).

-(3)(3) = -9

• Brackets indicate what the exponent should use. So if you would like for the exponent to see a negative base, remember to place the number inside a pair of brackets.

Multiplication Law of exponents. 

The multiplication law is simple.

• If the bases are the same number, all you have to do is add the exponents together and the base will stay the way it was.
• Example: = =
• If the bases are different numbers, the question does not fall into the multiplication law category and instead is thought of as a BEDMAS question.

Division Law of exponents. 

• The division law is similar to the multiplication law, but with different rules.
• Just like the multiplication law, only if the bases are same number, will this rule be successful.
• But instead of adding the exponents together, we subtract the exponents while using the division law.
• Example: = =
• If the bases are different numbers, this rule will not fall into the division law category and instead will also be thought of as a BEDMAS question.

Power of a Power Law.

• When you see a question that looks like this , you can use the power of a power law.
• All you have to do, is to multiply the two exponents (the exponent on the inside of the brackets and the exponent on the outside of the brackets).
• Example: = =

BEDMAS – When is an exponent question really a BEDMAS question?

• We use the BEDMAS technique when we are adding exponents and subtracting exponents, no matter what the base is. We also use BEDMAS when we are multiplying and dividing exponents, but only when the bases are different numbers. 
• Before we evaluate a BEDMAS question, we always need to remember the order of operations.

• In a question including brackets, we always do the work that is inside the brackets first. Example:

= = +

= 256 + 2 = 258

With any question using addition, subtraction, division or multiplication, that does not include brackets in the question, you always do the exponent work first and then evaluate the existing numbers using the symbol that is requested. Example:

= = 128