# 4.10 Proficiency exam

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This module is from Elementary Algebra by Denny Burzynski and Wade Ellis, Jr. Operations with algebraic expressions and numerical evaluations are introduced in this chapter. Coefficients are described rather than merely defined. Special binomial products have both literal and symbolic explanations and since they occur so frequently in mathematics, we have been careful to help the student remember them. In each example problem, the student is "talked" through the symbolic form.This module contains the proficiency exam for the chapter "Algebraic Expressions and Equations".

## Proficiency exam

( [link] ) In the expression below, specify the number of terms that are present, then list them.
$3a\left(a+1\right)-\left(a+2\right)\left(a-3\right)$

$\text{two:}\text{\hspace{0.17em}}\text{\hspace{0.17em}}3a\left(a+1\right),-\left(a+2\right)\left(a-3\right)$

( [link] ) List, if there are any, the common factors of
$20{x}^{3}{y}^{2}+15{x}^{3}{y}^{2}{z}^{2}+10{x}^{3}{z}^{2}$

$5{x}^{3}$

( [link] ) How many ${y}^{2}\left(b+2\right)\text{'}s$ in $8x{y}^{2}\left(b+2\right)\left(b-6\right)$ ?

$8x\left(b-6\right)$

( [link] ) Write the coefficient of ${x}^{3}$ in $8{x}^{3}{y}^{3}z$ .

$8{y}^{3}z$

( [link] ) Find the value of ${P}^{2}$ if $k=4$ and $a=3$ .
${P}^{2}=k{a}^{3}$

108

( [link] ) Classify the polynomial given below as a monomial, binomial, trinomial, or none of these. Specify the degree of the polynomial and write the numerical coefficient of each term.
$3{x}^{3}y+4x{y}^{4}+8{x}^{2}{y}^{2}{z}^{0}w,\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}z\ne 0$

trinomial; 5th degree;
numberical coefficients: 3, 4, 8

Simplify the algebraic expressions for the following problems.

( [link] ) $4{x}^{2}+3x+2x+11{x}^{2}-3$

$15{x}^{2}+5x-3$

( [link] ) $3a\left[2\left(a+1\right)+4\right]-18a$

$6{a}^{2}$

( [link] ) $\left(x+2\right)\left(x+4\right)$

${x}^{2}+6x+8$

( [link] ) $\left(3a-7\right)\left(2a+10\right)$

$6{a}^{2}+16a-70$

( [link] ) ${\left(y+3\right)}^{2}$

${y}^{2}+6y+9$

( [link] ) ${\left(6a+7y\right)}^{2}$

$36{a}^{2}+84ay+49{y}^{2}$

( [link] ) ${\left(4x-9y\right)}^{2}$

$16{x}^{2}-72xy+81{y}^{2}$

( [link] - [link] ) $3{x}^{2}\left(2x+5\right)\left(3x+1\right)$

$18{x}^{4}+51{x}^{3}+15{x}^{2}$

( [link] - [link] ) $\left(3a-b\right)\left(4a-3b\right)$

$12{a}^{2}-13ab+3{b}^{2}$

( [link] - [link] ) $-6{y}^{2}\left(2y+3{y}^{2}-4\right)$

$-18{y}^{4}-12{y}^{3}+24{y}^{2}$

( [link] - [link] ) $-4{b}^{3}{\left({b}^{2}-1\right)}^{2}$

$-4{b}^{7}+8{b}^{5}-4{b}^{3}$

( [link] - [link] ) ${\left(2{a}^{3}+3{b}^{2}\right)}^{2}$

$4{a}^{6}+12{a}^{3}{b}^{2}+9{b}^{4}$

( [link] - [link] ) $6a\left(a-2\right)-\left(2{a}^{2}+a-11\right)$

$4{a}^{2}-13a+11$

( [link] - [link] ) $\left(5h+2k\right)\left(5h-2k\right)$

$25{h}^{2}-4{k}^{2}$

( [link] - [link] ) Subtract $4{a}^{2}-10$ from $2{a}^{2}+6a+1$ .

$-2{a}^{2}+6a+11$

( [link] - [link] ) Add three times $6x-1$ to two times $-4x+5$ .

$10x+7$

( [link] - [link] ) Evaluate $6{k}^{2}+2k-7$ if $k=-1$ .

$-3$

( [link] - [link] ) Evaluate $-2m{\left(m-3\right)}^{2}$ if $m=-4$ .

392

( [link] ) What is the domain of $y=\frac{3x-7}{x+3}$ ?

$\text{all\hspace{0.17em}real\hspace{0.17em}numbers\hspace{0.17em}except\hspace{0.17em}}\left(-3\right)$

where we get a research paper on Nano chemistry....?
what are the products of Nano chemistry?
There are lots of products of nano chemistry... Like nano coatings.....carbon fiber.. And lots of others..
learn
Even nanotechnology is pretty much all about chemistry... Its the chemistry on quantum or atomic level
learn
da
no nanotechnology is also a part of physics and maths it requires angle formulas and some pressure regarding concepts
Bhagvanji
hey
Giriraj
Preparation and Applications of Nanomaterial for Drug Delivery
revolt
da
Application of nanotechnology in medicine
what is variations in raman spectra for nanomaterials
I only see partial conversation and what's the question here!
what about nanotechnology for water purification
please someone correct me if I'm wrong but I think one can use nanoparticles, specially silver nanoparticles for water treatment.
Damian
yes that's correct
Professor
I think
Professor
Nasa has use it in the 60's, copper as water purification in the moon travel.
Alexandre
nanocopper obvius
Alexandre
what is the stm
is there industrial application of fullrenes. What is the method to prepare fullrene on large scale.?
Rafiq
industrial application...? mmm I think on the medical side as drug carrier, but you should go deeper on your research, I may be wrong
Damian
How we are making nano material?
what is a peer
What is meant by 'nano scale'?
What is STMs full form?
LITNING
scanning tunneling microscope
Sahil
how nano science is used for hydrophobicity
Santosh
Do u think that Graphene and Fullrene fiber can be used to make Air Plane body structure the lightest and strongest. Rafiq
Rafiq
what is differents between GO and RGO?
Mahi
what is simplest way to understand the applications of nano robots used to detect the cancer affected cell of human body.? How this robot is carried to required site of body cell.? what will be the carrier material and how can be detected that correct delivery of drug is done Rafiq
Rafiq
if virus is killing to make ARTIFICIAL DNA OF GRAPHENE FOR KILLED THE VIRUS .THIS IS OUR ASSUMPTION
Anam
analytical skills graphene is prepared to kill any type viruses .
Anam
Any one who tell me about Preparation and application of Nanomaterial for drug Delivery
Hafiz
what is Nano technology ?
write examples of Nano molecule?
Bob
The nanotechnology is as new science, to scale nanometric
brayan
nanotechnology is the study, desing, synthesis, manipulation and application of materials and functional systems through control of matter at nanoscale
Damian
Is there any normative that regulates the use of silver nanoparticles?
what king of growth are you checking .?
Renato
What fields keep nano created devices from performing or assimulating ? Magnetic fields ? Are do they assimilate ?
why we need to study biomolecules, molecular biology in nanotechnology?
?
Kyle
yes I'm doing my masters in nanotechnology, we are being studying all these domains as well..
why?
what school?
Kyle
biomolecules are e building blocks of every organics and inorganic materials.
Joe
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