99.3k views
2 votes
A³+b³ if a+b=3ab=2
please help me​

1 Answer

1 vote

Answer:


a^3 + b^3 = -4

Explanation:

Given


a + b = 3ab = 2

Required

Solve:
a^3 + b^3

Rewrite the expression as:


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

Factorize


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


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

Rewrite as:


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


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

Factorize


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

Open brackets


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

Given that:


a + b = 3ab = 2

This means that:


a + b = 2 and
3ab = 2

So, we have:


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


a^3 + b^3 = 2^3 - 3 * 2 * 2


a^3 + b^3 = 8 - 12


a^3 + b^3 = -4

User Evilsanta
by
7.7k points

Related questions

1 answer
1 vote
129k views
asked Mar 6, 2024 185k views
PoulsQ asked Mar 6, 2024
by PoulsQ
8.0k points
1 answer
0 votes
185k views
1 answer
0 votes
214k views
Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.

9.4m questions

12.2m answers

Categories