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rosijanka [135]
3 years ago
13

(Picture) MULTIPLYING POLYNOMIALS AND SIMPLIFYING EXPRESSIONS PLEASE HELP!!!!

Mathematics
1 answer:
kvv77 [185]3 years ago
3 0

Answer:

Answer: Third option is the right answer.

Step-by-step explanation:

First we the write the expression

(a+b)(a^{2}+b^{2}-ab)

Now teacher says that the product of these polynomials will result in the sum of  a^{3}+b^{3}

Now the teacher ask if we put the value of a = 2x and b = 1 then what will be the expression look like.

(2x+1)\left [ (2x)^{2}+(1^{2})-(2x)(1)\right ]

=(2x+1)(4x^{2}+1-2x)

So third option is looking like our expression.

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Anyone knows how to do questions 7 and 8? 15 pts!!
Oksi-84 [34.3K]
7) Certainly there is a typo in the statement, just see that the expression of item (ii) is different from that of item (i). Probably the correct expression is: 2x^2-4x+5. With this consideration, we can continue.

(i) Let E the expression that we are analyzing:

E=2x^2-4x+5\\\\ E=2x^2-4x+2-2+5\\\\ E=2(x^2-2x+1)-2+5\\\\ E=2(x-1)^2+3

Since (x-1)² is a perfect square, it is a positive number. So, E is a result of a sum of two positive numbers, 2(x-1)² and 3. Hence, E is a positive number, too.

(ii) Manipulating the expression:

2x^2+5=4x\\\\ 2x^2-4x+5=0

So, it's the case when E=0. However, E is always a positive number. Then, there is no real number x that satisfies the expression.

8) Let E the expression that we want to calculate:

E=(2+1)(2^2+1)(2^4+1)\cdot ...\cdot(2^{32}+1)+1\\\\ E-1=(2+1)(2^2+1)(2^4+1)\cdot ...\cdot(2^{32}+1)

Multiplying by (2-1) in the both sides:

(2-1)(E-1)=(2-1)(2+1)(2^2+1)(2^4+1)\cdot ...\cdot(2^{32}+1)\\\\ (E-1)=\underbrace{(2-1)(2+1)}_{2^2-1}(2^2+1)(2^4+1)\cdot ...\cdot(2^{32}+1)\\\\ (E-1)=\underbrace{(2^2-1)(2^2+1)}_{2^4-1}(2^4+1)\cdot ...\cdot(2^{32}+1)\\\\ ... Repeating the process, we obtain: ...\\\\ E-1=(2^{32}-1)(2^{32}+1)\\\\ E-1=2^{64}-1\\\\ \boxed{E=2^{64}}
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3 years ago
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Answer:

D

Step-by-step explanation:

7 0
2 years ago
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Y= 3x+13<br> y=x-3 <br> How do you solve this equation?
ra1l [238]

Answer:

x=-5 & y=-2

Step-by-step explanation:

y= 3x+13

y= x-3

x-3=3x+13

-3=2x+13

-10=2x

x=-5

then

y=3(-5)+13

y=-15+13

y=-2

6 0
3 years ago
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A hungry college student just finished eating a large cheese and pepperoni pizza from​ Doug's Pizza Palace and felt there​ wasn'
maw [93]

Answer:  14

Step-by-step explanation:

  • Degrees of freedom is the number of values in the evaluation of a test statistic that are free to vary.

For t-statistic , the degree of freedom for a sample with sample size 'n' is given by :-

df=n-1

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Then, the number of degrees of freedom the t-value will have :-

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7 0
3 years ago
4x+10=-26 two-step equation
Nana76 [90]

Answer:

x = -9

Step-by-step explanation:

4x+10=-26

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4x = -36

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2 years ago
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