+0

# Precalculus

0
37
1

Find the x^4 term of (5x-3)^10

Guest Apr 6, 2018
Sort:

#1
+19207
0

Find the x^4 term of (5x-3)^10

$$\begin{array}{|rcll|} \hline && (5x-3)^{10} \\ &=& \dbinom{10}{0}(5x)^{10} +\dbinom{10}{1}(5x)^{9}(-3)^1 +\dbinom{10}{2}(5x)^{8}(-3)^2 +\dbinom{10}{3}(5x)^{7}(-3)^3\\ &+& \dbinom{10}{4}(5x)^{6}(-3)^4 +\dbinom{10}{5}(5x)^{5}(-3)^5 +{\color{red}{\dbinom{10}{6}(5x)^{4}(-3)^6}} + \ldots +\dbinom{10}{10}(-3)^{10} \\ \hline \end{array}$$

$$\text{x^4 term:}$$

$$\begin{array}{|rcll|} \hline && \dbinom{10}{6}(5x)^{4}(-3)^6 \\\\ &=& \dbinom{10}{10-6}5^4x^43^6 \\\\ &=& \dbinom{10}{4}3^65^4x^4 \\\\ &=& \dfrac{10}{4}\cdot \dfrac{9}{3}\cdot \dfrac{8}{2}\cdot \dfrac{7}{1}\cdot 3^65^4x^4 \\\\ &=& 10\cdot 3 \cdot 7 \cdot 3^65^4x^4 \\\\ &=& 2 \cdot 5\cdot 3 \cdot 7 \cdot 3^65^4x^4 \\\\ &=& 2\cdot 7\cdot 3^75^5x^4 \\\\ &=& 14\cdot 3^75^5x^4 \\\\ &=& 14\cdot 2187\cdot 3125 x^4 \\\\ &=& 95681250 x^4 \\ \hline \end{array}$$

heureka  Apr 6, 2018

### 14 Online Users

We use cookies to personalise content and ads, to provide social media features and to analyse our traffic. We also share information about your use of our site with our social media, advertising and analytics partners.  See details