Multiplying Binomials Using the FOIL Method

Day 1 - Multiplying Binomials

What if we have

 $\left(5x-9\right)\left(5x-7\right)$  ? There are 2 methods

• Distribute:  $5x\left(5x-7\right)\ \rightarrow\ 25x^2-35x$  

• Distribute:  $-9\left(5x-7\right)\ \rightarrow\ -45x+63$  

• Can we combine like terms?

•  $25x^2-80x+63$  

Multiple Choice

Practice

$$\left(3x-7\right)\left(4x+2\right)$$  

• $$7x^2+28x-6x+14$$  

• $$12x^2-22x-14$$  

• $$12x^2+6x-28x+14$$  

The other method - FOIL

 $\left(5x-9\right)\left(5x-7\right)$  

• F - First:  $\left(5x\right)\left(5x\right)$  

• O - Outside:  $\left(5x\right)\left(-7\right)$  

• I - Inside:  $\left(-9\right)\left(5x\right)$  

• L - Last:  $\left(-9\right)\left(-7\right)$  

Poll

$$\left(9x+2y\right)^2$$  What do we do here?

• $$81x^2+4y^2$$  

• $$\left(9x+2y\right)\left(9x+2y\right)$$  , then FOIL

• $$\left(11xy\right)^2$$  

Multiple Choice

$$\left(5ab-2\right)^2$$  

Practice:

• $$25ab^2+20ab-4$$  

• $$25ab-10ab-10ab+4$$  

• $$25ab^2-20ab+4$$  

Poll

$$\left(4m-2\right)\left(4m^2+5mn+3n^2\right)$$  

Can we FOIL this, or just use the distributive property?

• FOIL

• Distribute

 $\left(4m-2\right)\left(4m^2+5mn+3n^2\right)$  

•  $4m\left(4m^2+5mn+3n^2\right)$  

•  $-2\left(4m^2+5mn+3n^2\right)$