Transcript of Math 7 FACTORING ALGEBRAIC EXPRESSIONS. RECALL EXPANDING EXPRESSIONS Before, we used the...
- Slide 1
- Math 7 FACTORING ALGEBRAIC EXPRESSIONS
- Slide 2
- RECALL EXPANDING EXPRESSIONS Before, we used the Distributive
Property to expand an algebraic expression. Recall that the two
parts of the expression were called factors. For example, 3(2x + 9)
Since the two things are being multiplied together (using the
Distributive Property), the 3 and the 2x + 9 are said to be
factors
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- NEW TODAY Today, we will basically be doing the reverse of
Expanding. The reverse of expanding is Factoring. Think about the
result that you received on the previous slide when you expanded
the expression 3(2x + 9).6x + 27 What if I gave you 6x + 27 and
asked you to get back to the factored version? In other words, get
back to what it was prior to expanding it.
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- FACTORING EXPRESSIONS Think about 6x + 27. Look at the two
terms 6x and 27. What do you notice about both of them? Yesthey are
both divisible by 3. Thus, we say that they share a common factor
of 3. Since this is the case, you can factor out the 3 like this:
3( ) Since you factored out the three from both of the terms, what
is left in each term? To find this, simply divide both terms by
3.
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- FACTORING CONTINUED 6x + 27 and 3(2x + 9) are called equivalent
expressions because they are equal to each other, but they look
different. It is possible to have many different equivalent
expressions to the same expression
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- EQUIVALENT EXPRESSIONS For example: 12x + 24 has quite a few
expressions that are equivalent to it. Can you give me some? Also,
explain why they are equivalent 12(x + 2) is said to be the
simplest form of 12x + 24 because the greatest common factor or GCF
was factored out (12 is the largest factor that is in both 12 and
24)
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- EXAMPLES Create an equivalent expression to the following by
factoring out the common term 12x + 30 14 + 21x 72y 36 6p 45
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- MORE EXAMPLES 54y + 15x 9 8m 24 21p + 7
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- MAKE CERTAIN YOU ARE CORRECT How can we be sure that we have
correctly created an equivalent expression? Use the Distributive
Property to see if you get back to the original expression! This is
a great way to check that you are correct. Go back and see if this
works
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- FACTORING WITH FRACTIONS Obviously fractions and mixed numbers
will make things much more difficult. It will be more difficult
because it is tough to recognize what they will actually have in
common Take a look: What do they have in common?
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- FACTORING WITH FRACTIONS AND MIXED NUMBERS The first thing we
should do is convert all mixed numbers to improper fractions. It is
easier to deal with JUST FRACTIONS! would change to Looking at the
two fractions, what do they share? Would a common denominator help?
This would make it
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- FACTORING WITH FRACTIONS AND MIXED NUMBERS Taking a look at you
realize that they share. How do we come up with the inside? Divide,
remember? So you must do And you must do DROP SWITCH FLIP
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- FACTORING WITH FRACTIONS AND MIXED NUMBERS Thus, the factored
version would be: In actuality, there are in infinite amount of
equivalent expressions that we could come up with. We are
essentially free to take out whatever we want, because we can
always divide a fraction away from another fraction.lets take a
look at this concept on the next slide.
- Slide 14
- FACTORING WITH FRACTIONS AND MIXED NUMBERS
- Slide 15
- On a state test, you are more likely to see these as multiple
choice questions. If this is the case, the best way to approach
them is to just expand all of the choices out to see which one will
get you the original in return Example: Take a look at NYS Testing
Program Sample Questioncoming right up
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- EXAMPLE FROM NYS TEST
http://www.p12.nysed.gov/assessment/common-core-
sample-questions/math-grade-7.pdf
http://www.p12.nysed.gov/assessment/common-core-
sample-questions/math-grade-7.pdf Another Example: is equivalent to
which expression below? A) 4(5x + 2) B) C)