Multiplying binomial special cases

Multiplying binomial special cases

By Deb Scott

Let's Learn about Special Cases

• Perfect Squares

• Difference of squares

Perfect Squares:

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

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

(2x + 3)²

• 4x² + 12x + 9
• 4x² + 5x + 9
• 4x² + 10x + 9
• 4x² + 9

Multiple Choice

(x + 7)²

• x² + 14x + 49

• x² + 8x + 41

• x² + 16x + 41

• x² - 49

Multiple Choice

(x + 5)²

• x² + 10x + 25
• x² + 5x + 25
• x² + 6x - 10
• x² _6x + 25

Multiple Choice

Multiply

(3x - 10)²

• 9x² - 60x + 100

• 9x² + 60x + 100

• 9x² - 30x + 100

• 9x² + 30x + 100

Multiple Choice

(x - 6)^2

• x^2 - 12x + 36
• x^2 + 36
• x^2 - 36
• x^2 - 6x + 36

Multiple Choice

Simplify:
(x-7)²

• x²-49
• x²+49
• x²-14x+49
• x²-14x-49

Multiple Choice

(6y - 7) (6y + 7)

• 36y² - y - 49
• 36y² - 42y - 49
• 36y² + 84y - 49
• 36y² - 49

Multiple Choice

(x + 5) (x - 5)

• x² -10x + 25
• x² - 25x - 25 
• x² - 50x + 25
• x² - 25

Multiple Choice

(3x + 2) (3x - 2)

• 9x² - 4

• 9x²

• 3x² - 4

• 9x² + 4

Multiple Choice

Multiply

$$\left(2x\ -\ 8\right)^2$$  

• $$4x^2\ -\ 32x\ +\ 64$$  

• $$4x^2\ -\ 16x\ +\ 64$$  

• $$4x^2\ -\ 16$$  

• $$4x^2\ -\ 64$$  

Multiple Choice

Multiply

$$\left(5x\ +\ 2\right)^2$$  

• $$25x^2\ +\ 4x\ +\ 4$$  

• $$25x^2\ +\ 20x\ +\ 4$$  

• $$25x^2\ +\ 4$$  

• $$10x^2\ +\ 4$$