Multiplying Expressions

9/29: Multiply Expressions

Let's include multiplying when rewriting expressions!

What We've Seen...

We've seen distributing when combining like terms, but what about when we have to multiply by more than 1 term?

Multiple Choice

You know this part! Rewrite (x+2)(x-5) in standard form ax²+bx+c

• x²+3x-10

• x²-3x-10

• 2x²-5x

• x²-3x+10

How'd you do that??

We use the area model (the BOX) to organize those terms and see each term getting distributed to each other term.

We'll continue using this method when multiplying more complicating cases!

When it's a little tougher...

• We do the same thing!

• 1a) Set up one expression on the side of the area model

• 1b) Set up the other expression on the top of the area model

• 2) Distribute each term to each other term by filling out the area model

• 3) Combine your like terms! (Remember like=same variable and same power)

Let's do a crazy one together!

Write this example down in your notes!

Multiple Choice

You try this one! $$3x\left(4x+5\right)$$  

• $$12x^2+15x$$
  

• $$12x^2-15x$$
  

• $$12x+15x=27x$$
  

• $$3x\left(9x\right)=27x^2$$
  

Multiple Choice

Now try this one! (Draw it in your notes)  $$\left(x^2+5\right)\left(x^2-11x+6\right)$$  

• $$x^4-6x^2-49x+30$$  

• 
  

  $$x^4-11x^3+11x^2-55x+30$$  
  

• $$x^4-11x^3+6x^2-50x+30$$  
  

Multiple Choice

One more!  $$\left(x^2+4x+3\right)\left(2x^2-9x+7\right)$$

• $$2x^4-x^3-23x^2+10x+21$$  
  

• $$2x^4+17x^3+49x^2+46x+21$$  
  

• $$2x^4-17x^3+23x^2+46x+21$$