Month: April 2017

This week, we studied Difference of Squares.

It’s easy to tell if a question is a Difference of Squares question or not.

You can tell by whether or not it has a subtraction sign, and whether it’s a binomial, meaning there’s two terms.  In the following Difference of Squares equation, we must solve and expand it.

 − 36

We’ll take the and put the individual coefficients in separate brackets like this:

(p  )(p  )

Next, we take 36, and do the square root of it.

= 6

So, we’re left with 6.

Now, we’re going to incorporate the 6 into our new equation.

We need to use zero pairs, so one six is going to be left as a positive, and the other as a negative.

Our final, expanded equation will look like this:

(p – 6)(p + 6)

So when you use the distributive property, or the claw, you’ll get  – 36.

How to Factor GCF:

1. See if you can divide all numbers in the equation with the same number.
2. With the first equation above, we can see that 3, 6, and 9 can all be divided by 3.
3. From there, we put the GCF into the equation.  We put it in front of an open bracket to start off the equation.  Like this: 3(
4. Then, we divide each number by the number we put in front of the open bracket.  3 divided by 3, equals one, so we just place to co-efficient there instead of a 1 in front of it, because the co-efficient by itself indicates that there is a one before it.
5. 9 divided by 3 equals 3, so we replace the 9 with a 3, and now we have 3, plus the co-efficient behind it.
6. 6 divided by 3 equals 2, so we replace the constant, 6, with 2.
7. There we have it, a complete equation.  You can see other examples I’ve created in the picture above.

 

This week, we started talking about polynomials.  I learned how to make equations out of symbols and vice-versa.

First, I wrote out the symbols.  The big, coloured in boxes represent positive x squared.  The white big boxes represent negative x squared.  The long skinny black pieces represent positive x, and the white ones represent negative x.  The small pieces mean a whole number; black meaning positive, and white representing negative.  If we eliminate the zero pairs, we get out equation.  Zero pairs mean there’s a pair of positive and negative symbols.  If we remove them all, we get three big, coloured in squares (3x squared), two white skinny pieces (-2x), and three small white pieces (-3).  So, our equation would look similar to this: