SOLUTION: i need help solving this equation.
4(16a^4-56a^2+49)=
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Question 251561: i need help solving this equation.
4(16a^4-56a^2+49)=
Found 2 solutions by jim_thompson5910, stanbon:
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
This is equivalent to factoring
Start with the given expression
Factor out the GCF
Now let's focus on the inner expression
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Looking at we can see that the first term is and the last term is where the coefficients are 16 and 49 respectively.
Now multiply the first coefficient 16 and the last coefficient 49 to get 784. Now what two numbers multiply to 784 and add to the middle coefficient -56? Let's list all of the factors of 784:
Factors of 784:
1,2,4,7,8,14,16,28,49,56,98,112,196,392
-1,-2,-4,-7,-8,-14,-16,-28,-49,-56,-98,-112,-196,-392 ...List the negative factors as well. This will allow us to find all possible combinations
These factors pair up and multiply to 784
1*784
2*392
4*196
7*112
8*98
14*56
16*49
28*28
(-1)*(-784)
(-2)*(-392)
(-4)*(-196)
(-7)*(-112)
(-8)*(-98)
(-14)*(-56)
(-16)*(-49)
(-28)*(-28)
note: remember two negative numbers multiplied together make a positive number
Now which of these pairs add to -56? Lets make a table of all of the pairs of factors we multiplied and see which two numbers add to -56
| First Number | Second Number | Sum | | 1 | 784 | 1+784=785 |
| 2 | 392 | 2+392=394 |
| 4 | 196 | 4+196=200 |
| 7 | 112 | 7+112=119 |
| 8 | 98 | 8+98=106 |
| 14 | 56 | 14+56=70 |
| 16 | 49 | 16+49=65 |
| 28 | 28 | 28+28=56 |
| -1 | -784 | -1+(-784)=-785 |
| -2 | -392 | -2+(-392)=-394 |
| -4 | -196 | -4+(-196)=-200 |
| -7 | -112 | -7+(-112)=-119 |
| -8 | -98 | -8+(-98)=-106 |
| -14 | -56 | -14+(-56)=-70 |
| -16 | -49 | -16+(-49)=-65 |
| -28 | -28 | -28+(-28)=-56 |
From this list we can see that -28 and -28 add up to -56 and multiply to 784
Now looking at the expression , replace with (notice adds up to . So it is equivalent to )
Now let's factor by grouping:
Group like terms
Factor out the GCF of out of the first group. Factor out the GCF of out of the second group
Since we have a common term of , we can combine like terms
So factors to
So this also means that factors to (since is equivalent to )
note: is equivalent to since the term occurs twice. So also factors to
------------------------------------------------------------
So our expression goes from and factors further to
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Answer:
So factors to
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
i need help solving this equation.
----
It is not an equation as there is nothing in the right side.
--------
4(16a^4-56a^2+49)
---
It is a perfect trinomial with variable a^2:
= 4(4a^2 + 7)(4a^2-7)
---
= 4(4a^2+7)(2a-sqrt(7))(2a+sqrt(7))
=========================================
Cheers,
Stan H.
=
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