Mathematics Middle School

How do i solve this question, please help and pls explain
a³x - x⁴ + a²x² - ax³

Answers

Answer 1

Answer:

[tex]\huge\boxed{x(a-x)(a+x)^2}[/tex]

Step-by-step explanation:

In order to factor this expression, our goal is to write the expression in a way that we can factor out a term.

With the expression [tex]a^3 x - x^4 + a^2 x^2 - ax^3[/tex], we need to note an exponent rule.

[tex]a^{b+c} = a^b a^c[/tex]

Step 1:

We can use this to get each term of this expression to have a term of [tex]x[/tex] so we can factor it out.

Let's look at each term and get it so that we can factor out an x term.

[tex]a^3 x = x a^3[/tex] (Commutative Property)[tex]x^4 = xx^3[/tex] (Since [tex]x^3 \cdot x^1 = x^4[/tex])[tex]a^2 x^2 = a^2 \cdot xx[/tex] (Since [tex]x^2 = x \cdot x[/tex])[tex]ax^3 = a \cdot xx^2[/tex] (Since [tex]x^3 = x^2 \cdot x^1[/tex]

With this, our equation becomes [tex](xa^3) - (xx^3) + (xxa^2) - (xx^2a)[/tex].

We now can factor out the common term x.

[tex]x(a^3 - x^3 + xa^2 - x^2a)[/tex]

Step 2:

From here, we can now factor [tex]a^3 - x^3 + xa^2 - x^2 a[/tex]

Rearrange the equation: [tex]a^3 +xa^2 - x^3 - x^2a[/tex] Factor out [tex]a^2[/tex] from [tex]a^3 + xa^2[/tex]  which comes out to be  [tex]a^2(a+x)[/tex] Factor out [tex]-x^2[/tex] from [tex]-x^3 - x^2a[/tex] which comes out to be [tex]-x^2(x+a)[/tex] We now have [tex]a^2(a+x) - x^2(x+a)[/tex] Factor out the common term, [tex](a+x)[/tex], which comes out to be [tex](a+x)(a^2 - x^2)[/tex] Factor [tex]-x^2+a^2[/tex] into [tex](a+x)(a-x)[/tex] We now have [tex](a+x) (a+x) (a-x)[/tex], which is simplified to [tex](a-x)(a+x)^2[/tex]

Finalizing:

Since we have just factored [tex]a^3 - x^3 + xa^2 - x^2 a[/tex]  and factored x out of [tex]a^3 x - x^4 + a^2 x^2 - ax^3[/tex] in the first couple of steps, we need to have it as a factorization of x.

[tex]x(a-x)(a+x)^2[/tex]

Hope this helped!

Related Questions

I need help ASAP
Solve: 8x - 6x - 25 = -35

Answers

8x-6x= 2x-25=-35 add +25 to -35= -10/2x your answer should be x= -5

True or False?

The following relation represent a function.

Question 4 options:
True
False

Answers

Answer: it would be false.

Step-by-step explanation:

Answer:

false

Step-by-step explanation:

im in k 12 and just took it.

54.36 ÷ 0.5


please explain how to do it

Answers

Answer:

108.72

Step-by-step explanation:

first you have to see how many .5 goes into 50 than you have to see how many .5 goes into 4than you have to see how many .5 goes into 36 because .5 cant go into .3

Answer:

well the answer is 108.72

Step-by-step explanation:

well you can turn them into fractons then it would have to do the keep change flip thing and it would be 1359 / 25 times 2/1 and you would get 108.72oh yeah um you have to turn the 54.36 into a fraction and it would be 1359/25 and 0.5 would be 1/2 so you would just time those together but like you have to flip 1/2 to2/1 then multiply them and like yeah

My last question today is what is b in y=mx+b?

Answers

Answer:

It's the y-intercept of the equation

Step-by-step explanation: b is the y-intercept and just in case you wanted to know, m is the slope

Answer:

the y is the intersept

mx =slope

please answer its a multiple question answer

Answers

The answers 1, 2, 4, and 5 are right

Hope this helps

Step-by-step explanation:

1st and 2nd, and 4th and 5th are equivalent to -11/4

3rd and 6th are not the same thing.

Which values from the given replacement set make up the solution set of the inequality?

Answers

Answer:

Can you put a picture because I don’t understand what your trying to say

Step-by-step explanation:

Ethan drove his car to his grandparents’ house at a steady rate of 54 miles per hour. The table shows the distance Ethan had driven based on the time that had passed.

Time (hours)​
1
2
1
1
1
2
2
2
1
2
3
Distance (miles)​ 27 54 81 108 135 162
​If the distance traveled by Ethan for different amounts of time is plotted on a graph and a line is drawn through all the points, what will you notice?
​Will all the points on the line make sense in the given problem situation? Why or why not?

Answers

Answer: a linear line

Step-by-step explanation:

it’s going to be a linear line going straight up :)

The Answer is a loner line

What is the sales tax on a jacket priced at ​$350 if the sales tax rate is 7​%?

Answers

$105, first find 7% of 350 by multiplying it by 0.7 then you would get 245 and then subtract that by 350 which is 105
Multiply 350 by .07 (move decimal over 2 places to the left). I got 24.5 as my answer. Subtract 24.5 from 350 and the final price of the jacket is $325.50

ANSWER: sales tax: $24.50
final price of jacket: $325.50

78 fl oz = _c = _oz
pls help me and its in us coustemery units

Answers

Answer:78 fl oz= 9.75c =81.12 oz

Step-by-step explanation:

78fl oz = 9.75c = 81.12 oz
Hope this is right!! ☺️

100 POINTS!! I NEED THIS KNOWW!!!!

The number line shows the distance in meters of two birds, A and B, from a worm located at point X:

A horizontal number line extends from negative 3 to positive 3. The point labeled as A is at negative 2.5, the point 0 is labeled as X, and the point labeled B is at 2.5.

Write an expression using subtraction to find the distance between the two birds.

Show your work and solve for the distance using additive inverses.

Answers

Answer:

So if bird A is at -2.5 and bird B is at 2.5, then it's 2 I think

Step-by-step explanation:

I think this is right, sorry if it's not.

Answer:

2.5- -2.5 is 0

Step-by-step explanation:

Last question for today

Answers

Answer:

u can use a graphing caluclator

Step-by-step explanation:

Answer:

oooooooooooooooooooooooooooooooo

Step-by-step explanation:

y -3 =9 solve for y 4w = 24 solve for w y -3 =9 solve for y

Answers

Y=12
Add 3 to both sides add nine and 3 to get 12

W=6
Divide both sides by four divide 24 by 4 to get six

X=2
Subtract eight from both sides
subtract eight from 10 to get 2

drag the fractions that is equivalent to each repeating decimal each fractions may be used only once​

Answers

Answer:

0.23 = 7/30

0.4 = 4/9

1.6 = 5/3

3.5 = 32/9

Step-by-step explanation:

I'm 100% that this is correct

5-2(x+5)=3x-15 solve for X

Answers

Answer:

x= 2

Step-by-step explanation:

5 -2(x +5)= 3x -15

Expand:

5 -2x -2(5)= 3x -15

5 -2x -10= 3x -15

Simplify:

-2x -5= 3x -15

Bring x terms to 1 side, constant to the other:

3x +2x= 15 -5

5x= 10

Divide both sides by 5:

x= 10 ÷5

x= 2

Answer:

Step-by-step explanation:

x=2

The price of candy at The Candy Stop can be determined by the equation
p = 2.95n, where p is the price and n is the number of pounds of candy. What is the constant of proportionality?

Group of answer choices

$2.95/pound

$8.85/3 pounds

$5.90/2 pounds

$1/pound

Answers

Answer:

5.90/2 pounds

Step-by-step explanation:

$5.90/2 pounds I hope this helps

What is the value of the opposite of (-6 3/4
PLS GUYS I NEED HELP DO NOT STEAL MY POINTS ):

Answers

Answer:

c i think

Step-by-step explanation:

also hi

Barb needs to run a total of 9 miles each wee. So for, she has run 4 miles this week. How much father does she need to run? Write an equation and solve to focus put how many miles she needs to run.

Answers

Answer:

Wouldn't the answer be 5 because 4 plus 5 is 9?

Answer:

yEs daddyy ebdbbxbdbdvdhsbehsjdjehdbdbevdbebshshs

Tonya bought a blanket for ​$​32.87, a pillow for ​$11.25​, and a baseball cap for ​$17.75. She paid ​$60 and the rest she borrowed from her friend. If she got ​$8.13 in change from the​ cashier, how much did she borrow from her friend to pay for all the​ items?

Answers

Answer:

6.26

Step-by-step explanation:

Answer:

1.35

Step-by-step explanation:

this 33.35+11.25+16.75-60 is what you do in order to get the answer

Find the elapsed time
1:12 p.m. to 8:11 p.m.
A. 7 h 1 minute
B. 7 h 59 minutes
C. 6 h 59 minutes

Answers

C. 6hr 59 minutes cause if you subtract 8:11-1:12 it’s 6 59
C all u have to do is subtract the 1:12 from the 8:11

which of the following ratios are proportional? help me, please

Answers

Answer:

12/15 and 16/20

Step-by-step explanation:

Ratios are proportional if they represent the same relationship. One way to see if two ratios are proportional is to write them as fractions and then reduce them. If the reduced fractions are the same, your ratios are proportional.

12/15 simplified is 4/5.

16/20 simplified is 4/5

12/15 and 16/20 are proportional

i need help with prob #2 on this

Answers

Answer:

x and y are not in direct variation.

Step-by-step explanation:

Direct Variation

Two variables x and y have a direct proportion or variation if:

y = k.x

Where k is the factor of proportionality. The value of k must be constant for every ordered pair (x,y). If only one of them does not have the very same k, then the relationship is not direct.

The value of k can be solved from the equation:

[tex]\displastyle k=\frac{y}{x}[/tex]

Let's substitute the given points in the table:

(2,8)

[tex]\displastyle k=\frac{8}{2}=4[/tex]

k = 4

(4,16)

[tex]\displastyle k=\frac{16}{4}=4[/tex]

k = 4

(6,30)

[tex]\displastyle k=\frac{30}{6}=5[/tex]

k = 5

Since the value of k is not constant, then x and y are not in direct variation.

Math problem. I need help plz.

Answers

Answer:

Never because one of them goes 1k8 and one of them goes 24 so if they that song every time then it would be the same time diffrence even if you try a million tinmes

Step-by-step explanation:

It’s never, they would never play again

Need help asap. Alebra 1 Thanks so much to whoever answers

Answers

Answer:

Concept: Algebra

(0,1) is the point at x= 0 and y=1 Hence the graph b^x at 0 must always be 1 hence the statement is TRUE

Answer:

(0,1) is the point at x= 0 and y=1

Hence the graph b^x at 0 must always be 1 hence the statement is TRUE

Graph the point that has the coordinates -4 1/2, 2 1/5. Please help!

Answers

Answer: you should use desmos grapgh caculater

Step-by-step explanation:

Please answer please!! Please answer 1–4 please actually answer please I need thissss

Answers

1. 75% increase
2. 30% decrease
3. 80% increase
4. 25% decrease

300 hotdogs and hamburgers total. Hotdogs cost $2. Hamburgers cost $3. How many hamburgers? How many hotdogs?

Answers

Answer:

75 and 50

Step-by-step explanation:

A nursery owner buys 5 panes of glass to fix some damage to her greenhouse. The 5 panes cost ​$11.75. ​Unfortunately, she breaks 2 more panes while repairing the damage. What is the cost of another 2 panes of​ glass?

Answers

Answer:

$5.90

Step-by-step explanation:

$4.70 because 11.75/5=2.35 and 2.35 x2 more panes= 4.7

PLS HELP I WILL GIVE BRAINLIEST WHOMEVER HAS A APPROPRIATE LEGIT ANSWER

Answers

Answer:

9

Step-by-step explanation:

answer

step by step explanation

Use the divisibility rules to determine which of the following numbers 528 is divisible by. (Check all that apply.)


6
3
5
7
10
2
11
9
4

Answers

The numbers that are divisible to 528 is 1,2,3,4,6,8,11,12,16,22,24,33,44,48,66,88,132,264,528

Which algebraic expression represents the verbal expression “7 decreased by m”?
A) m - 7
B) 7m
C) 7 - m
D) 7 + m

Answers

c. 7-m because you’re taking m away from 7
The answer is c 7 - m
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