Answer:
Solution: x³ + 3x² + 3x + 1
Step-by-step explanation:
Take a look at the following Pascal's Triangle:
(x + y)⁰ = 1
(x + y)¹ = 1x + 1y
(x + y)² = 1x² + 2xy + 1y²
(x + y)³ = 1x³ + 3x²y + 3xy² + 1y³
(x + y)⁴ = 1x⁴ + 4x³ + 6x²y² + 4xy³ + 1y⁴
As you can see our binomial is '(x + 1)³.' Therefore we expand the expression with respect to the third row in the Pascal's Triangle, (x + y)³ = 1x³ + 3x²y + 3xy² + 1y³. The procedure would be as follows:
(x + 1)³ = 1x³ + 3(x)²1 + 3x(1)² + 1(1)³ = x³ + 3x² + 3x + 1
OK, because it is asking you to subtract a (negative) number and two negatives make a positive, the question would be -56 + 27.07 = ? with some simple addition, the answer would be <span>-28.93.
I hope this helps :)</span>
Answer:
\frac{d}{dx}\left(\frac{1+x^4+x^6}{x^2+x+1}\right)=\frac{4x^7+5x^6+8x^5+3x^4+4x^3-2x-1}{\left(x^2+x+1\right)^2}
Step-by-step explanation:
Answer:
a^3 + a^2
Step-by-step explanation:
Distribute the term left of each set of parentheses, then combine like terms.
-a²(3a - 5) + 4a(a² - a) =
= -3a^3 + 5a^2 + 4a^3 - 4a^2
= a^3 + a^2
Check the picture below.
so the volume will simply be the area of the hexagonal face times the height.
![\textit{area of a regular polygon}\\\\ A=\cfrac{1}{4}ns^2\stackrel{\qquad degrees}{\cot\left( \frac{180}{n} \right)}~~ \begin{cases} n=\stackrel{number~of}{sides}\\ s=\stackrel{length~of}{side}\\[-0.5em] \hrulefill\\ n=6\\ s=12 \end{cases}\implies A=\cfrac{1}{4}(6)(12)^2\cot\left( \frac{180}{6} \right) \\\\\\ A=216\cot(30^o)\implies A=216\sqrt{3} \\\\[-0.35em] ~\dotfill\\\\ \stackrel{\textit{area of the hexagon}}{(216\sqrt{3})}~~\stackrel{height}{(10)}\implies 2160\sqrt{3}~~\approx ~~3741.2~cm^3](https://tex.z-dn.net/?f=%5Ctextit%7Barea%20of%20a%20regular%20polygon%7D%5C%5C%5C%5C%20A%3D%5Ccfrac%7B1%7D%7B4%7Dns%5E2%5Cstackrel%7B%5Cqquad%20degrees%7D%7B%5Ccot%5Cleft%28%20%5Cfrac%7B180%7D%7Bn%7D%20%5Cright%29%7D~~%20%5Cbegin%7Bcases%7D%20n%3D%5Cstackrel%7Bnumber~of%7D%7Bsides%7D%5C%5C%20s%3D%5Cstackrel%7Blength~of%7D%7Bside%7D%5C%5C%5B-0.5em%5D%20%5Chrulefill%5C%5C%20n%3D6%5C%5C%20s%3D12%20%5Cend%7Bcases%7D%5Cimplies%20A%3D%5Ccfrac%7B1%7D%7B4%7D%286%29%2812%29%5E2%5Ccot%5Cleft%28%20%5Cfrac%7B180%7D%7B6%7D%20%5Cright%29%20%5C%5C%5C%5C%5C%5C%20A%3D216%5Ccot%2830%5Eo%29%5Cimplies%20A%3D216%5Csqrt%7B3%7D%20%5C%5C%5C%5C%5B-0.35em%5D%20~%5Cdotfill%5C%5C%5C%5C%20%5Cstackrel%7B%5Ctextit%7Barea%20of%20the%20hexagon%7D%7D%7B%28216%5Csqrt%7B3%7D%29%7D~~%5Cstackrel%7Bheight%7D%7B%2810%29%7D%5Cimplies%202160%5Csqrt%7B3%7D~~%5Capprox%20~~3741.2~cm%5E3)
