Multiplying Polynomials (Special Cases)

Multiplying Polynomials

Poll

Where are you now? How well could you tackle this: (2x+5)(x-1)?

• Confident - I could do this on my own. Ready for a quiz or test.

• Getting there - I think I understand, but I need more practice.

• Struggling - It's difficult for me to multiply without direct help.

• Clueless - Even with help, and watching the videos, I have no idea what to do.

Multiple Choice

Give it a try: (2x+5)(x-1)

• $2x^2+3x-6$

• $2x^2+3x-5$

• $2x^2+7x+5$

• $2x^2-3x-5$

Poll

How did you do?

• Got it, correct. Ready to move on!

• I made an arithmetic error.

• I just guessed.

• Thought I had it, and I'm not sure what I did wrong.

Let's Learn about Special Cases

• Perfect Squares

• Difference of squares

Perfect Squares:

Example

 $\left(x+3\right)^2$  
First, rewrite it as (x+3)(x+3)
Next, distribute. Check your answer on the next slide.

Multiple Choice

Multiply:

 $\left(x+3\right)^2$  

**Start by rewriting as (x+3)(x+3)**

•  $x^2+6x+9$  

•  $x^2+9$  

•  $x^2+3x+9$  

•  $x^2+6x+6$  

Let's try a few more...

Multiple Choice

(x + 5)² 

Hint: try (x + 5)(x + 5)

• x² + 25
• x² + 10x + 25
• x² + 10 x + 10
• x² + 10

Multiple Choice

 $(5a+2b)^2\ =\ 25a^2+20ab+4b^2$ 
**Test it out, don't just guess!!**

• TRUE

• FALSE

Multiple Choice

Simplify:

(x-7)²

• x²-49

• x²+49

• x²-14x+49

• x²-14x-49

Open Ended

What patterns do you notice about perfect squares?

Multiple Choice

Now give this one a try:

Multiply (5x-3)(5x+3)

• 25x²-15x-9

• 25x²+15x-9

• 25x²-9

• 25x²+9

Open Ended

What happens when you combine like terms on this problem?

(5x-3)(5x+3)

Multiple Choice

Simplify.

(2b − 6)(2b + 6)

• 4b² − 24b − 36

• 4b² − 36

• 2b² − 36

• 4b − 36

Multiple Choice

Simplify.

(y − 5)(y + 5)

• y² + 25

• y² + 10y + 25

• y² − 10y + 25

• y² − 25

Let's Recap...

• We're still multiplying and distributing!

• When a binomial factor is squared, rewrite the factor to set up a distribution problem. This will give you a perfect square trinomial.

• When two factors are the same except for the sign in the middle, the middle terms cancel, resulting in a "difference of squares."

Multiple Choice

Think backwards...which solution below would multiply to give you: $a^2-10a+25$ ? (Hint:  multiply out the answer choices, or think about patterns.)

•  $\left(a-5\right)\left(a+5\right)$  

•  $\left(a+5\right)^2$  

•  $\left(a-5\right)^2$  

•  $\left(a-10\right)^2$  

Multiple Choice

Think backwards...which solution below would multiply to give you  $x^2-121$ ?

•  $\left(x-11\right)^2$  

•  $\left(x+11\right)\left(x-11\right)$  

•  $\left(x-60.5\right)\left(x+60.5\right)$  

•  $\left(x+11\right)^2$  

Poll

Where are you now? After today's lesson, where would you rate yourself on multiplying? Examples:

 $\left(x+3\right)\left(2x+7\right),\ \left(2x+1\right)^2,\ or\ \left(3x+1\right)\left(3x-1\right)$  

• Feeling good, could take a test on it now.

• It's making more sense. I could probably use a little more practice.

• I understand a little, but I still need a lot of help.

• I have no idea how to do any of this, even with help.