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Grade 8 - Mathematics
7.22 Formula for a3 - b3

Example: Divide (a3 - b3) by (a - b).
Solution:

     a2 + ab + b2

a - b | a3 + ...+...- b3

a3 - a2b


  

     a2b

      

     a2b - ab2


ab2 - b3
ab2 - b3

 

0

Quotient = a2 + ab + b2.
Division Rule:  Dividend = Quotient * Divisor + Reminder.
a3 - b3 = (a2 + ab + b2)(a - b) + 0
 = (a2 + ab + b2)(a - b)
\a3 - b3 = (a2 + ab + b2)(a - b)

Directions: Solve the following division problems usning above formula and show your work. Also write at least ten examples of your own.
Q 1: Divide [(7a)3-(6b)3] by (7a-6b).
49a2+42ab+36b2
49a3+42ab+36b3
49a2-42ab+36b2

Q 2: Divide [(9a)3-(8b)3] by (9a-8b).
81a3+72ab+64b3
81a2+72ab+64b2
81a2-72ab+64b2

Q 3: Divide [(15a)3-(6b)3] by (15a-6b).
225a3+90ab+36b3
225a2-90ab+36b2
225a2+90ab+36b2

Q 4: Divide [(5a)3-(6b)3] by (5a-6b).
25a2+30ab+36b2
25a3+30ab+36b3
25a2-30ab+36b2

Question 5: This question is available to subscribers only!

Question 6: This question is available to subscribers only!


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