1. 4.3 Factoring a Difference of Squares and Cubes

2. I) Review: Conjugate of a Binomial
To find the conjugate of a binomial, you switch the sign between the two terms
Positive  Negative
Negative  Positive
Ex: Find the Conjugate:

3. Q: What happens when you multiply a binomial with its conjugate?
Ex: Expand the following
1. The middle two terms will always cancel each other out
2. The first and last terms are always perfect squares
3. The middle sign is always a subtraction

4. Ex: Indicate what the missing terms are:

5. II) Factoring a Difference of Squares
Difference  Subtraction
Difference of Squares  Subtraction of two perfect squares
Sometimes to use the difference of squares formula, you need to factor out a common factor from both terms first
When asked to factor “Completely”, you are to factor the expression until it can not be factored anymore

6. Ex: Factor completely

7. Challenge: Factor
Can’t Factor!! Not a Difference

8. Discuss: Which step does the first mistake appear?
Dividing both sides by a-b means dividing by 0 since a=b
Can’t divide by zero! Becomes undefined

9. Sum and Difference of Cubes:
Expand the following:
Combine Like-Terms
Some of the terms will cancel each other out

10. Factoring each sum/Difference of Cubes

11. Ex: Evaluate:

12. Ex: Given that “p” is a prime number, solve for “x”:
Let “p” equal to 5 – x
So “x’ is equal to –8 and the prime “p” is 13