Lesson 89 – Doodles Do Algebra

lesson89doodlepigcToday 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.