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### Grade 7 - Mathematics4.48 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+36b249a2-42ab+36b249a3+42ab+36b3 Q 2: Divide [(15a)3-(6b)3] by (15a-6b).225a3+90ab+36b3225a2+90ab+36b2225a2-90ab+36b2 Q 3: Divide [(9a)3-(8b)3] by (9a-8b).81a2+72ab+64b281a3+72ab+64b381a2-72ab+64b2 Q 4: Divide [(5a)3-(6b)3] by (5a-6b).25a2+30ab+36b225a2-30ab+36b225a3+30ab+36b3 Question 5: This question is available to subscribers only! Question 6: This question is available to subscribers only!

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