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3 years ago

How do the expressions 4(3+x) and (3+3+3+3) + (x+x+x+x) compare to one another

Mathematics

2 answers:

valina [46]3 years ago

6 0

Answer:

Well they represent the same answer as the second expression is the distributive property of the first expression.

Step-by-step explanation:

4(3+x) is basically 4 • (3+x)since we are working with addition and multiplication you can use the distributive property. That can be written out as (4•3) + (4•x). If you wanted to simplify it even more then it could be written as (3+3+3+3) + (x+x+x+x)

Dafna1 [17]3 years ago

3 0

Answer:

Step-by-step explanation:

If we expand 4(3+x), we get (4*3)+(4*x).

Then we do 4*3 to get 12 and 4*x to get 4x

(3+3+3+3) is the same thing as 4*3, because we are adding 3 together 4 times. (3+3+3+3) gives us 12 as well, since they are the same thing.

(x+x+x+x) is the same thing because we are adding x together 4 times, which is the same thing as (4*x). (x+x+x+x) gives us 4x as well.

Hope this helps.

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TIMED PLEASE HURRY HELP WITH 2 EASY QUESTIONS

Alex_Xolod [135]

<h2> Question # 1</h2><h2>Which statements are true?</h2><h2 /><h3><u>Analyzing and solving the first statement:</u></h3>

$4g^2-g=g^2\left(4-g\right)$

Solving the expression

$4g^2-g$

$\mathrm{Apply\:exponent\:rule}:\quad \:a^{b+c}=a^ba^c$

$g^2=gg$

So,

$4gg-g$

$\mathrm{Factor\:out\:common\:term\:}g$

$g\left(4g-1\right)$

So,

$4g^2-g:\quad g\left(4g-1\right)$

Therefore, the statement $4g^2-g=g^2\left(4-g\right)$ is NOT CORRECT.

<h3><u>Analyzing and solving the second statement:</u></h3>

$35g^5-25g^2=\:5g^2\left(7g^3-5\right)$

Solving the expression

$35g^5-25g^2$

$\mathrm{Apply\:exponent\:rule}:\quad \:a^{b+c}=a^ba^c$

$g^5=g^3g^2$

So,

$35g^3g^2-25g^2$

$\mathrm{Rewrite\:}25\mathrm{\:as\:}5\cdot \:5$

$\mathrm{Rewrite\:}35\mathrm{\:as\:}5\cdot \:7$

$5\cdot \:7g^3g^2-5\cdot \:5g^2$

$\mathrm{Factor\:out\:common\:term\:}5g^2$

$5g^2\left(7g^3-5\right)$

So,

$35g^5-25g^2=\:5g^2\left(7g^3-5\right)$

Therefore, the statement $35g^5-25g^2=\:5g^2\left(7g^3-5\right)$ is CORRECT.

<h3><u>Analyzing and solving the third statement:</u></h3>

$24g^4+18g^2=\:6g^2\left(4g^2+3g\right)$

<h3 />

Solving the expression

<h3> $24g^4+18g^2$ </h3><h3> $24g^2g^2+18g^2$ </h3><h3> $\mathrm{Rewrite\:}18\mathrm{\:as\:}6\cdot \:3$ </h3><h3> $\mathrm{Rewrite\:}24\mathrm{\:as\:}6\cdot \:4$ </h3><h3> $6\cdot \:4g^2g^2+6\cdot \:3g^2$ </h3><h3> $\mathrm{Factor\:out\:common\:term\:}6g^2$ </h3><h3> $6g^2\left(4g^2+3\right)$ </h3>

So,

<h3> $24g^4+18g^2=6g^2\left(4g^2+3\right)$ </h3>

Therefore, the statement $24g^4+18g^2=\:6g^2\left(4g^2+3g\right)$ is CORRECT.

<h3><u>Analyzing and solving the fourth statement:</u></h3>

$9g^3+12=\:3\left(3g^3+4\right)$

Solving the expression

$9g^3+12$

$\mathrm{Rewrite\:}12\mathrm{\:as\:}3\cdot \:4$

$\mathrm{Rewrite\:}9\mathrm{\:as\:}3\cdot \:3$

$3\cdot \:3g^3+3\cdot \:4$

$\mathrm{Factor\:out\:common\:term\:}3$

$3\left(3g^3+4\right)$

So,

$9g^3+12=\:3\left(3g^3+4\right)$

Therefore, the statement $9g^3+12=\:3\left(3g^3+4\right)$ is CORRECT.

<h2> Question # 2</h2><h2>Which expressions are completely factored?</h2>

<u>Solving first expression</u>

Considering the expression

$30a^6-24a^2$

$30a^6-24a^2$

$30a^4a^2-24a^2$

$\mathrm{Rewrite\:}24\mathrm{\:as\:}6\cdot \:4$

$\mathrm{Rewrite\:}30\mathrm{\:as\:}6\cdot \:5$

$6\cdot \:5a^4a^2-6\cdot \:4a^2$

$\mathrm{Factor\:out\:common\:term\:}3a^2$

$3a^2\left(10a^4-8\right)$

Thus, the expression $30a^6-24a^2=3a^2\left(10a^4-8\right)\:$ is completely factored.

<u>Solving second expression</u>

Considering the expression

$12a^3-8a$

$12a^3-8a$

$\mathrm{Apply\:exponent\:rule}:\quad \:a^{b+c}=a^ba^c$

$a^3=a^2a$

So,

$12a^2a-8a$

$\mathrm{Rewrite\:}8\mathrm{\:as\:}4\cdot \:2$

$\mathrm{Rewrite\:}12\mathrm{\:as\:}4\cdot \:3$

$4\cdot \:3a^2a-4\cdot \:2a$

$\mathrm{Factor\:out\:common\:term\:}4$

$4\left(3a^3-2a\right)$

Thus, the expression $12a^3-8a=\:4\left(3a^3-2a\right)$ is completely factored.

<u>Solving third expression</u>

$16a^5-20a^3\:\:\:\:\:\:\:\:\:\:\:\:$

$16a^5-20a^3$

$\mathrm{Apply\:exponent\:rule}:\quad \:a^{b+c}=a^ba^c$

$a^5=a^2a^3$

So,

$16a^2a^3-20a^3$

$\mathrm{Rewrite\:}20\mathrm{\:as\:}4\cdot \:5$

$\mathrm{Rewrite\:}16\mathrm{\:as\:}4\cdot \:4$

$4\cdot \:4a^2a^3-4\cdot \:5a^3$

$\mathrm{Factor\:out\:common\:term\:}4a^3$

$4a^3\left(4a^2-5\right)$

Thus, the expression $16a^5-20a^3\:=4a^3\left(4a^2-5\right)$ is completely factored.

<u>Solving fourth expression</u>

$24a^4+18$

$24a^4+18$

$\mathrm{Rewrite\:}18\mathrm{\:as\:}6\cdot \:3$

$\mathrm{Rewrite\:}24\mathrm{\:as\:}6\cdot \:4$

$6\cdot \:4a^4+6\cdot \:3$

$\mathrm{Factor\:out\:common\:term\:}6$

$6\left(4a^4+3\right)$

Thus, the expression $24a^4+18=6\left(4a^4+3\right)$ is completely factored.

Keywords: expression, factoring

Learn more about expression factoring from brainly.com/question/14051207

#learnwithBrainly

8 0

3 years ago

What is the solution to the equation? 3x - 5 =7x -9

Alecsey [184]

Answer:

x=1

Step-by-step explanation:

3x - 5 =7x -9

Subtract 3x from each side

3x - 5-3x =7x-3x -9

-5 = 4x-9

Add 9 to each side

-5+9 = 4x-9+9

4 = 4x

Divide each side by 4

4/4 = 4x/4

1=x

5 0

3 years ago

Read 2 more answers

Please answer this question !! 20 points and brainliest !!

lawyer [7]

Answer: b.2x

Step-by-step explanation:

why? because 2 can be divided into all of the numbers evenly!

all the numbers have (x)

it wouldn't be (2x^2) ,because one of the numbers have x^3

5 0

3 years ago

Read 2 more answers

Complete the inequality statement with the symbol that makes it true.

OLga [1]

Equal because these numbers are of the same value

7 0

3 years ago

If you get this correct I will give you brainlest 5 stars and thanked please help on it

sweet-ann [11.9K]

Answer:

6:7 is 24:x

6:7is18:y

24/6=4. 4*7=28!

Therefore 24 : 28

18/6=3. 3*7=21.

Therefore 18:21

Please brainlest and thanks and 5 star rating! Your welcome and I am so happy to help you!

Step-by-step explanation:

5 0

3 years ago