Which statement describes the construction being illustrated on the rectangle shown (look at pic)

Solved

Show answers

Ответ:

xXwolfieplayzXx

29.10.2022

Mathematics

You build Pascal's triangle as follows: every row starts and ends with 1, and every term is the sum of the two immediately above. So, we have

$\begin{array}{c}n=0\\n=1\\n=2\\n=3\\n=4\end{array}\qquad\begin{array}{ccccccccc}&&&&1&&&&\\&&&1&&1&&&\\&&1&&2&&1&&\\&1&&3&&3&&1&\\1&&4&&6&&4&&1\end{array}$

We can use this triangle to expand powers as follows: the binomial (a+b)^n will feature all the powers a^xb^y , where x+y=n , with some coefficients: in this case, we have

(a+b)^4 = c_4a^4b^0 + c_3a^3b^1+c_2a^2b^2+c_1a^1b^3+c_0a^0b^4

and the coefficients c_i are exactly the required row of the Pascal's triangle. Removing also unnecessary exponents, we have

(a+b)^4 = a^4 + 4a^3b+6a^2b^2+4ab^3+b^4

Finally, substitute a=2x and b=4y to get the

(2x+4y)^4 = 16 x^4 + 128 x^3 y + 384 x^2 y^2 + 512 x y^3 + 256 y^4

0,0(0 оценок)

Ask your question to the AI advisor

Ai-bot is an expert in any field and is the perfect companion for reliable and useful answers and advice on a variety of topics, including science, history, technology, art, sports, health, culture and more.

Ask your question

More tips

Answers on questions: Mathematics

Ask an AI advisor a question

I want advice