# Express as a polynomial. (3u-1)(u+2)+7u(u+1)

Express as a polynomial. (3u-1)(u+2)+7u(u+1)
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Step 1
Given expression:
(3u-1)(u+2)+7u(u+1)
Step 2
Now,
A polynomial function is expressed as: ${a}_{n}{x}^{n}+{a}_{n-1}{x}^{n-1}+\dots +{a}_{1}x+{a}_{0}$
where ${a}_{0},{a}_{1},\dots ..{a}_{n}$ be a real numbers and ${a}_{n}\ne 0$ and n be a non negative integer.
Expand:
(3u-1)(u+2)+7u(u+1)=3u(u+2)-1(u+2)+7u(u)+7u
$=3u\left(u\right)+6u-u-2+7{u}^{2}+7u$
$=3{u}^{2}+6u-u-2+7{u}^{2}+7u$
$=\left(3{u}^{2}+7{u}^{2}\right)+\left(6u-u+7u\right)-2$
$=10{u}^{2}+12u-2$
Therefore,
Required polynomial is $10{u}^{2}+12u-2$

Dawn Neal
Consider the expression
(3u-1)(u+2)+7u(u+1)
This can be written as
(3u+(-1))(u+2)+(7u)(u+1)
=(3u)(u)+(3u)(2)+(-1)(4)+(-1)(2)+(7u)(u)+(7u)(1)
[Using distributive property]
$=3{u}^{2}+6u-u-2+7{u}^{2}+7u$ [Multiplying]
$=\left(3+7\right){u}^{2}+\left(6-1+7\right)u-2$ [Adding the terms of like power of x]
$=10{u}^{2}+12u-2$ [Simplifying]
Hence, the required polynomial is
$10{u}^{2}+12u-2$