Question

(a^3-b^3)(a^3+b^3)(a^6+b^6)

Answer 1

применим формулу разность квадратов

(a+b)(a -b)= a²- b²

(a³- b³)(a³+b³)(a⁶+b⁶)= (a⁶-b⁶)(a⁶+b⁶)= (a¹² -b¹²)

Answer 2

It seems like you've provided an algebraic expression. If you'd like, I can help you simplify or expand this expression. The expression you've given is:

(a^3 - b^3)(a^3 + b^3)(a^6 + b^6)

If you want to expand this expression, you can use the distributive property (FOIL) multiple times to simplify it. Let's break it down step by step:

Step 1: Expand the first two factors using the difference of cubes formula (a^3 - b^3 = (a - b)(a^2 + ab + b^2)):

(a^3 - b^3)(a^3 + b^3) = (a - b)(a^2 + ab + b^2)(a^3 + b^3)

Step 2: Multiply the result from Step 1 by the third factor (a^6 + b^6):

(a - b)(a^2 + ab + b^2)(a^3 + b^3)(a^6 + b^6)

Step 3: Use distributive property to combine the terms in each pair of factors:

(a - b)(a^5 + a^4b + a^3b^2 + a^3b^3 + ab^4 + b^5)(a^6 + b^6)

Step 4: Distribute the remaining factors:

a^11 + a^10b + a^9b^2 + a^9b^3 + a^5b^6 - a^6b + a^5b^2 + a^4b^3 + a^10b^6 + a^9b^7 + a^8b^8 + a^8b^9 + a^4b^10 + a^3b^11 + ab^12 - b^7

So, the fully expanded expression is quite lengthy and involves many terms:

a^11 + a^10b + a^9b^2 + a^9b^3 + a^5b^6 - a^6b + a^5b^2 + a^4b^3 + a^10b^6 + a^9b^7 + a^8b^8 + a^8b^9 + a^4b^10 + a^3b^11 + ab^12 - b^7

Please double-check the steps and terms to ensure accuracy, as manual calculations can sometimes lead to errors. If you have any further questions or if there's anything else I can assist you with, feel free to ask!