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3241004551 [841]
2 years ago
15

What is 8y squared+7y+4-3(2y squared-5y-8)?

Mathematics
1 answer:
Aneli [31]2 years ago
6 0

Answer:  2 • (y2 + 11y + 14)

Step-by-step explanation:

Changes made to your input should not affect the solution:

(1): "y2"   was replaced by   "y^2".  1 more similar replacement(s).

STEP

1

:

Equation at the end of step 1

 (((8•(y2))+7y)+4)-(3•((2y2-5y)-8))

STEP

2

:

Trying to factor by splitting the middle term

2.1     Factoring  2y2-5y-8  

The first term is,  2y2  its coefficient is  2 .

The middle term is,  -5y  its coefficient is  -5 .

The last term, "the constant", is  -8  

Step-1 : Multiply the coefficient of the first term by the constant   2 • -8 = -16  

Step-2 : Find two factors of  -16  whose sum equals the coefficient of the middle term, which is   -5 .

     -16    +    1    =    -15  

     -8    +    2    =    -6  

     -4    +    4    =    0  

     -2    +    8    =    6  

     -1    +    16    =    15  

Observation : No two such factors can be found !!

Conclusion : Trinomial can not be factored

Equation at the end of step

2

:

 (((8•(y2))+7y)+4)-3•(2y2-5y-8)

STEP  

3

:

Equation at the end of step

3

:

 ((23y2 +  7y) +  4) -  3 • (2y2 - 5y - 8)

STEP

4

:

STEP

5

:

Pulling out like terms

5.1     Pull out like factors :

  2y2 + 22y + 28  =   2 • (y2 + 11y + 14)  

Trying to factor by splitting the middle term

5.2     Factoring  y2 + 11y + 14  

The first term is,  y2  its coefficient is  1 .

The middle term is,  +11y  its coefficient is  11 .

The last term, "the constant", is  +14  

Step-1 : Multiply the coefficient of the first term by the constant   1 • 14 = 14  

Step-2 : Find two factors of  14  whose sum equals the coefficient of the middle term, which is   11 .

     -14    +    -1    =    -15  

     -7    +    -2    =    -9  

     -2    +    -7    =    -9  

     -1    +    -14    =    -15  

     1    +    14    =    15  

     2    +    7    =    9  

     7    +    2    =    9  

     14    +    1    =    15  

Observation : No two such factors can be found !!

Conclusion : Trinomial can not be factored

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Step-by-step explanation:

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Subtract 1111 from both sides

5{e}^{{4}^{x}}=22-115e​4​x​​​​=22−11


 

Simplify 22-1122−11 to 1111

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Divide both sides by 55

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Use Definition of Natural Logarithm: {e}^{y}=xe​y​​=x if and only if \ln{x}=ylnx=y

{4}^{x}=\ln{\frac{11}{5}}4​x​​=ln​5​​11​​



 

: {b}^{a}=xb​a​​=x if and only if log_b(x)=alog​b​​(x)=a

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Use Change of Base Rule: \log_{b}{x}=\frac{\log_{a}{x}}{\log_{a}{b}}log​b​​x=​log​a​​b​​log​a​​x​​

x=\frac{\log{\ln{\frac{11}{5}}}}{\log{4}}x=​log4​​logln​5​​11​​​​



 

Use Power Rule: \log_{b}{{x}^{c}}=c\log_{b}{x}log​b​​x​c​​=clog​b​​x
\log{4}log4 -> \log{{2}^{2}}log2​2​​ -> 2\log{2}2log2

x=\frac{\log{\ln{\frac{11}{5}}}}{2\log{2}}x=​2log2​


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