Asked by Kimmie
Simplify (3x-2)^3 - (4x+5)^2
Can you show it step-by-step please
Can you show it step-by-step please
Answers
Answered by
Steve
You need the Binomial Theorem:
(a+b)^n = a^n + n a^(n-1) b + ...
So, you have
(3x-2)^3
= (3x)^3 - 3(3x)^2(2) + 3(3x)(2^2) - 2^3
= 27x^3 - 54x^2 + 36x - 8
(4x+5)^2
= (4x)^2 + 2(4x)(5) + 5^2
= 16x^2 + 40x + 25
Subtract them to get
27x^3 - 70x^2 - 4x - 33
(a+b)^n = a^n + n a^(n-1) b + ...
So, you have
(3x-2)^3
= (3x)^3 - 3(3x)^2(2) + 3(3x)(2^2) - 2^3
= 27x^3 - 54x^2 + 36x - 8
(4x+5)^2
= (4x)^2 + 2(4x)(5) + 5^2
= 16x^2 + 40x + 25
Subtract them to get
27x^3 - 70x^2 - 4x - 33
There are no AI answers yet. The ability to request AI answers is coming soon!
Submit Your Answer
We prioritize human answers over AI answers.
If you are human, and you can answer this question, please submit your answer.