Math help?

Question

ok so im stuck on what the problem is asking me to do?
so this direction says to factor and check by multuplying

here 2 problems
9y+21

14a+35b

what is it asking me to do?


and how do you collect like terms?
these are the problems 17c+6c

and 3y+7x+5y

please explain how to do the problems and include the answers to them as well
thanx in advance

Answer 1

In the first two it is asking you to divide out the largest common factor. So for 9y+21, you can take out 3, because 9y and 21 are each divisible by 3...this is what you would end up with:
3(3y + 7)
If you multiply that out you'll get what you started with. second example, 14a + 35b, you can take out 7, so:
7(2a + 5b)

In the second set, they just want you to add together the terms that will add, so in the first example, since 17c and 6c are both expressed in terms of c, you can just add them together to get:
23c.
In the second set, 3y and 5y are both in terms of y, but 7x is in terms of x. 5y and 3y add to give you 8y, but the 7x can't be added into that...so you get:
8y + 7x.

Good luck!

Answer 2

I guess you must mean factorize and then expand (multiplying) it again.

Well, in the first case: 9y + 21

To factorize, you must find a common factor of each term in the expression. That factor would be 3 as the coefficient 9 and the constant 21 is both divisible by 3, so therefore it would be written as follows: 3(3y+7) and to check, you simply multiply the outer number by each term within the brackets - 3x3y + 3x7 = 9y + 21, which is the original expression.

The number outside the brackets is always the highest common factor of the coefficient/constant (coefficient if there is a variable or constant if not) of each term.

The same procedure applies to the next one:

14a + 35b = 7(2a+5b) as 14 and 35 are both divisible by 7.

Again, when multiplying (expanding) the factorized expression, you perform it as follows:

7x2a + 7x5b = 14a + 35b as above.

Collecting like terms is simply adding the coefficients of the terms whose variables are the same. So in the case of 17c + 6c, both terms contain some variable c, so the simplified version of it is just 23c.

How did I get that? Well, previously there were the factorization of expressions so this isn't much different:

17c + 6c = c(17+6) = 23c (basically taking out a common factor of 'c' as they appear in both terms of the expression)

For 3y+7x+5y, as you may have noticed, there are two terms whose variables are y, these are the like terms and may be added as shown with the previous problem.

So 3y+7x+5y = 7x + y(3+5) = 7x + 8y

And there you have it. Hope this helps and good luck!

Answer 3

the first one 9y+21 factor is to break it down to the simplest form basically you find something that goes into both pieces. the only thing that goes into both 9 and 21 is 3. so you devide 9 by 3 and you get 3 then divide 21 by 3 and you get 7. you have to keep the letter with the number though.
the answer would be 3(3y+7) to multiply it you multiply the 3 to both the 3y and 7 and you would come back to 9y+21.
the second one is the same as the first to find what goes into both. the only thing that goes into both is a 7 so it be 7(2a+5b) you are just changing the numbers.
the third one you just add like ones. 17c+6c would be 23c.
3y+7x+5y would be 8y+7x. You cannot add the 7x to 8y because they are different. if you need more help you can message me at soccer_4_8

Answer 4

9y+21....if u notice then both the terms of the expression are multiples of 3...so just take 3 in common and slev as follows
3(3y+7)
since the terms in the brackets have prime number coeffiients, no further factorization can be done. hence the expression has been factored and the answer is 3(3y+7)
now to check by multiplying...simply open the brackets and multiply the number outside the brackets with each of the terms inside...so
3*3y+3*7
=9y+21
which is the same expression that u started out with...so the answer is checked
similarly u can solve 14a+35b
7(2a+5b)...this is the answer
to check
7*2a+7*5b
=14a+35b

Answer 5

look at 9y+21 what do they have in common and write it out:

9y is really 3 times 3 times y
and 21 is 3 times 7
now the only thing both have in common is one three so bring it out and write the remaining factors in parenthesis like this:

3(3y+7)

14a+35b is 7 times 2 times a plus 5 times 7 times b
the 7 is common to both so:

7(2a+5b) is the answer

to check your answer do the reverse to get the original problem back as an answer:

3(3y+7)= 3 times 3y plus 3 times 7 which becomes:
9y+21

and
7(2a+5b) is 7 times 2a plus 7 times 5b to get:
14a + 35b

For part 2 I would like to present a little way of doing it that may sound stupid but it works, remember to put the animals with the animals and fruit with the fruit.

if c stood for cherries then you have, 17 cherries plus 6 cherries, the result is 23 cherries or 23c.

if y is yaks and x is oranges then you have
3y+7x+5y, that is 3 yaks, plus 7 oranges, plus 5 yaks = 8 yaks and 7 oranges
8y + 7x

the idea is to add or subtract numbers with similar letters together.

Answer 6

9y+21

=3(3y+7)

14a+35b

=7(2a+5b)

17c+6c

=23c

3y+7x+5y

=8y+7x

Answer 7

To factorise, you just need to find the like term.
9y+21--------------3 is the highest like term, so
3(3y+7) -------------is the answer.

14a+35b----------------7 is the highest like term, so
7(2a+5b)-------------is the answer

17c+6c--------------- c is the only term they have in common, so
c(17+6) ------------------is the answer

3y+7x+5y -------------y is the like term in this one.
y(3+5)+7x----------------is the answer. the 7x doesnt have a like term, so just add it on the end like that.

Hope it helps, and didnt confuse you more