# Lesson 89 – Doodles Do Algebra

Today is more practice in factoring polynomials with two more rules to learn: divisibility rules for $a^4-b^4$ and $a^3+b^3$, and also how to abstract those rules to higher powers of a and b.

1. $(m+n)(m+n)$

2. $(a-bx)(a-bx)$

3. $(2x-5z)(2x-5z)$

4. $(x+y)(x-y)$

5. $(3m+4n)(3m-4n)$

6. $(ab+cd)(ab-cd)$

7. $(x)(a^2-x^2)=(x)(a+x)(a-x)$

8. $(y+1)(y^2-y+1)$

9. $(x-1)(x^2+x-1)$

10. $(2a-3b)(2^2a^2-4a*3b-3^2b^2)=(2a-3b)(4a^2-12ab-9b^2)$ here you need to recognize that 8 is 2 cubed and 27 is 3 cubed and then it all can be treated as x cubed minus y cubed and your can apply the general formula from lesson 88

11. $(a+b)(a^4-a^3b+ab^3-b^4)$

12. $(a+b)(a-b)(a^4-a^2b^2+b^4)$

these last few problems require a bit of thinking power and some long division, but other than that they are not hard.