The Internet

Log In or Register

Pascal's Triangle image with the expanded and simplified form of (-3x + 5)^4

Ask AI on The Internet

Question: Use Pascal's Triangle to expand and simplify (-3x + 5)4.

Asked by daoxlol192

0 Points

Log In or Register to Vote

Sure, I can guide you through the process. First, remember that the fourth line of Pascal's Triangle is 1, 4, 6, 4, 1. When you use the Binomial Theorem, the formula (a+b)^n = Σ (n choose k) * a^(n-k) * b^k, where k ranges from 0 to n, the coefficients (or multipliers) are the same as in the corresponding line of Pascal's Triangle. Here, a = -3x, b = 5, and n = 4. Remember that "n choose k" is equivalent to the entries in Pascal's Triangle. Now plug these values in to get the following terms: - For k = 0, the term is (4 choose 0)*(-3x)^(4-0)*5^0 = 1*(-3x)^4*1 = 81x^4. - For k = 1, the term is (4 choose 1)*(-3x)^(4-1)*5^1 = 4*(-3x)^3*5 = -540x^3. - For k = 2, the term is (4 choose 2)*(-3x)^(4-2)*5^2 = 6*(-3x)^2*25 = 1350x^2. - For k = 3, the term is (4 choose 3)*(-3x)^(4-3)*5^3 = 4*(-3x)*125 = -1500x. - For k = 4, the term is (4 choose 4)*(-3x)^(4-4)*5^4 = 1*625 = 625. When you add these together, the expanded and simplified form of (-3x + 5)^4 is 81x^4 - 540x^3 + 1350x^2 - 1500x + 625.

Answered by gpt-4

July 24, 2023, 8:56 a.m.

0 Points

Log In or Register to Vote

Think your answer is better than the AI's? Post it below.

Please log in or sign up to post your answer.

Question Tags
This article was generated in part by one of OpenAI’s large-scale language-generation model, answering user daoxlol192's question. Images were generated with OpenAI's AI model, DALL·E 2. The Internet takes ultimate responsibility for the content of this publication.
If you want your question answered by an AI, click here.

Published: Monday, July 24, 2023

Comment Section