What is the use of a bracket?
4 (x + 3)
4 (x + 3) (x + 3)
4 (x + 3)squared
When can you open out a bracket and when is it not allowed?
What is the differences in the following?
log 4
log 4x
log 4x + 3
log (4x + 3)
log (4x + 3)squared
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57 comments:
the use of a bracket is simply to group terms together.eg:
4(x+3) means '4' multiply by 'x+3'
without the brackets, it would mean somthing totally different... 4x + 3.
you can't open the brackets right away in 4(x+3)squared.
it is easier to work with writing it as 4 (x+3)(x+3).
using brackets simply means to perform what ever action in the bracket fisrt example 2( 3x + 4)squared
2(3x+ 4) (3x+4)
Brackets are punctuation marks used in pairs to set apart or interject a value within other value. they can denote coordinates, determine the order in which a sum must be done,intervals etc.
the difference of the given examples
*log4 means the log of 4
*log4x means the log of 4 multiplied by an unknown
*log4x + 3 means the sum of log4x and 3
*log(4x+3) means log of 4x+3
*log(4x+3)squared means the log of the square of 4x+3
brackets are used to separate terms it also means to multiply
the use of bracket is to indicate sign of multiplication and you can only open them when whatever is outside has been multiplied inside the brackets .example 8(2x + 5)is equal to 16x + 40
brackets is used to distinguish what numbers involved in the brackets are to be solved in an arithmetic calculation.
brakets can be use to group nurmbers that is similar in terms of variables. also it can be used to expand an equation when solving and making it smaller when simplifing.
brackets are used to differentiate between different operations and the sequence they are to be initiated.
brackets can be used, for example, when multypling negative and positive integers and also for dividing. it can be used in the BODMAS function. it is not allowed when only using the arithmetic on one value. eg.
4 x 3 + 1 = 5 correct
4 x( 3+1) = 16 wrong
Brackets are used for several applications. One application of brackets is it indicates a term to be multiplied by another term before or after it. Brackets are also used to group terms. In addition brackets can be used to make a calculation that has many terms easier by grouping them.
4(x+3) means 4x + 4x3
The other two problems are the same in that the last problem is a simplified version of the second problem.
Please note dat brackets have meaning...Having brackets mean sumting totally different from not having brackets. it is also important dat u know when 2 open out brackets. with respect to the first question. 4 (x + 3) is not the same as 4 X x + 3 since with the brackets we wud get 4x + 12 and without the brackets we wud get 4x + 3. considering 4 (x + 3)squared..we wud have two totally different answers if we multiply 4 into the brackets then square the answer than if we square the brackets first then multiply by 4. The latter method is correct.
the bracket is used to simplify the equation, instead of having the equation 4x + 12 it is easy to factorise and group the terms together
brackets can be used to express an equation by showing the order by which it should be executed.
e.g. in using the equation 4 x 2 + 6 to get a result of 32, without the brackets, automatically one would multiply 4 x 2 then add six to the answer, this would give s result of 14, but by placing the brackets to get: 4 x (6+2), one would then firstly add 6 and 2 then multiply the answer by 4
A rule u must remember is
this
(a+b)Squared=aSquared+2ab+bSquared
(x+3)Squared =(x+3)(x+3)
= xSquared+6x+3Squared
= xSquared+6x+9
the use of brackets is used to seperate terms.. brackets would be important to expand especially if it is to a power.. 4(x+3)squared = 4(x+3)(x+3).... the brackets must be opened n expanded firstly....
The use of bracket to me is considered to be multiplication this can say you have to multiply without the use of the multiplication sign
the brackets are used in order for us to seperate terms in a certain equation, so that we don't get confused with the positive and negative signs, in that equation.
the () is there to show that the term outside the () is supposed to be multiplied by each term in the ()
in the case of the brackets squared you are supposed to mutiply the () by itself.
brackets are used to seperate terms and symbolise that the expression in the brackets should be done first (BODMAS). also when removing brackets you have to multiply whatever was in the bracket by what is outside of the bracket
there are many uses of the bracket 1 way may be used to eliminate the multiplication sign e.g 2(3)= 6 or more commonly 2(x+3) which as the spartan said '2 multiply by x+3'
in the second case of 4(x+3)(x+3) the brackets indicates by the process of BODMASS multiplying (x+3)(x+3) which is x2+6x+9 then multiplying this result by 4 so we get 4(x2+6x+9)
Whenever I see a question where brackets are involved I direct my thoughts to the law of BODMAS.
4(x+3) squared means 4(x+3)(x+3)
=4(xsquared+3x+3x+9)
=4xsquared+6x+9
So you see folks First you need to expand the squared part then remove the brackets.
when removing brackets take in consideration that if there is a negative number infront of a bracket that number is multiplied by the equation in the bracket and the sign changes , example -4(3x+2)
is = -12x-8.
the term 4(x + 3)sqared means that the term in the brackets is multiplied twice.IE (x+3)is multiplied twice.
4(x+3)(x+3)........
first , simplify the brackets.use the term F.O.I.L. which means that u multiply thhe first term , then multiply the outside terms, then multiply the inside terms.when this is simplified, then multiply the 4. the same for the third sum. for the 1st sum, multiply the 4 by x then by 3.
cruiser ... i tink your calculation was slightly wrong ... the expansion of the brackets was correct whereu sed 4(x^2 + 6x + 9) however u must remember that u hav to multiply each term in the brackets by 4 .... so the ansa becomes 4x^2 + 24x + 36...
log 4 means the log of 4 to base 10
log 4x means the log of 4 multiply by x to base 10
log 4x + 3 means log of 4 multiply by x to base 10 add log 1000 (since log of 1000 to base 10 is 3)
log (4x + 3)means log of 4x +3 to base 10
log (4x + 3)squared means 2 log of 4x +3 to base 10
BRACKETS ARE USED TO REPRESENT MULTIPLICATION OF WHAT IS OUTSIDE THE BRACKET TO EACH TERM INSIDE THE BRACKET.
e.g 3(5+2)
this means - 3*5 + 3*2
P.S. don sristobal...you need to use smaller words please. explain it to me in layman terms
brackets can be used to group numbers or variables that have similar factors. for example,,
3x + 4x = x(3+4)
x here is common between the two variables. therefore it is pulled outside of the brackets and. when multiplied to each term inside the brackets, you should get back
3x + 4x
if i havn't explained F.O.I.L. this means First Outside Inside Last.this mens the 1st terms are multiplied 1st then the outside terms then the inside terms then multiply the last.
when there is something such as log4, it must be assumed that it is to the base of ten. therefore i agree with sparkle when she stated that everthing was to the base ten. the logs
log (4x + 3)squared can be expanded and solved.
opening a bracket is allowed when it is raised to a power or it is accompanied by a term to be mulitplied . Brackets are used to group terms.
i think brackets are used to group terms that need to be multiplied or divided by a certain variable.correct me if am wrong
bootz i tink u need to revise ur maths a bit. as sparkle said log 4 means the log of 4 to base 10. dats all.
log 4x means log 4 + log x..the laws!!..log 4x + 3 can be expressed as log 4 + log x + 3log[10]10
log (4x + 3) is not the same as log 4x + 3. since it is in brackets it is classified as 1 term. so we can put 10[x] = 4x + 3.im not so sure.
log (4x + 3)squared means that u firstly remove the bracket by squaring(4x + 3 after which u wud follow the same method as u did in working out log 4x + 3. im not so sure about dis whole ting. can sum1 tell me if im correct??
kervin!!ur confusing me.. care to break it down abit? any1!!!
in the case of log(4x+3)squared, can it be expresses as 2log(4x+3)?
sum1 care to explain the difference between log 4x + 3 and
log (4x + 3)??? im really confused!!!wat if u had 2 solve for x in the 2 questions below wat wud u get????
1)log 4x + 3 = 10
2)log (4x + 3) = 10
coke i dont know the difference but i could use some help with this also
Everyons seems to have the same idea that i want to share, in one, form or annother. the brackets in a question is used to separate tearms which are to be multiplied by each other. in doing so shortens the statement and makes it easyer to solve. since multiplication is understood, It it reduces errors in solveing equations as long as the BODMAS rule is used.
However i cant think of an example to demonstrate when it cant or shouldn't be used!? If someone can clear that up that would be greate. When shouldn't brackets be expanded.
The use of a bracket is too group like terms together. for example: when u have 2x + 4x this is also equal to 2x(1 + 2) also 2xy + 4 ax is also equal to 2x (y + 2a)
could an equation such as
X^[2] + 5X + 6 be simplified ?
well if so, how can this be used in getting results and even sketching a graph ?
Now, is y^(6X + 1) the same as:
(y^6)^X + y
or (y^6) + (y^X) + y ?
removing the brackets in logs can be tricky and if not careful can result in many errors so its usually best if the brackets are not removed unless its necessary
the use of the bracket is to group terms. It also means another way of multiplying items
Example: 2(3)= 6 is the same as
2 * 3 = 6
so i have to answer my own question???? after reading most of the comments i tink i cud solve it. i tink log 4x + 3 = 10 can be solved by
log 4x + 3 = 10
log 4x = 7
4x = 10[7]
and so on.....
log (4x + 3) = 10 can be solved by
4x + 3 = 10[10]
4x = 97
and so on.....
everyone agree????
the bracket makes the difference, with respect to the types of muliplying, therefore without the brackets it would be a complete different equation, like 4x +3
hey i have something not related to the use of brackets why is minus by a minus gives a plus say -10 apples by - 10 apples how can that give u 100 apples explain?????
Well "my_light" i really dont know, but dats just a rule in math..just accept that. a positive and a positive will always be a positive, a negative and a positive will always be a negative and a negative and a negative will always be a positive ok..
The use of brakets is to multiply what ever in the brakets by what ever is out side the brakets
log (4x = 3) ^2 the log rules state that log x ^2 is written as 2 log x.
keeping in mind wit wat i jus said ... does log (4x+3) sq mean that ( 4x + 3 ) must be squared first then everything in the brackets log..... if that is so then it is totally contradicting the rule befor don't you think
Brackets are used basically to group more than one terms together. It could also mean the same as a multiplication sign.
eg. 2(7)=2x7=14
6(2+8)=6(10)=60
4(3x+6)=4(3x)+4(6)=12x+24
The terms in Brackets must be simplified first before the outside can be worked out as shown in example 2.
If there remains more than one terms in the brackets after simplification then the term outside can be considered as a common factor and therefore must be multiplied by each and every term inside the brackets as shown in eg. 3!
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