SOLUTION: How would you simplify a problem such as (4t + 7)^2? I was thinking that what you would do is regroup it by first writing it as (4t-7)* (4t-7)and then from there grouping the two

Algebra ->  Square-cubic-other-roots -> SOLUTION: How would you simplify a problem such as (4t + 7)^2? I was thinking that what you would do is regroup it by first writing it as (4t-7)* (4t-7)and then from there grouping the two       Log On


   

Question 253687: How would you simplify a problem such as (4t + 7)^2?
I was thinking that what you would do is regroup it by first writing it as (4t-7)* (4t-7)and then from there grouping the two 4ts together and the -7's together; like this (16t)* (49). From there I was thinking that you would then try and get t by itself so that I could solve for it and that to do that I would need to divide 16 from both sides so that the resulting answer would be something like t(49/16). Would that be right?
Found 2 solutions by Alan3354, jim_thompson5910:
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
How would you simplify a problem such as (4t + 7)^2?
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= 16t^2 + 56t + 49

Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

%284t%2B7%29%5E2 Start with the given expression.


%284t%2B7%29%284t%2B7%29 Expand. Remember something like x%5E2=x%2Ax.


Now let's FOIL the expression.


Remember, when you FOIL an expression, you follow this procedure:


%28highlight%284t%29%2B7%29%28highlight%284t%29%2B7%29 Multiply the First terms:%284t%29%284t%29=16t%5E2.


%28highlight%284t%29%2B7%29%284t%2Bhighlight%287%29%29 Multiply the Outer terms:%284t%29%287%29=28t.


%284t%2Bhighlight%287%29%29%28highlight%284t%29%2B7%29 Multiply the Inner terms:%287%29%284t%29=28t.


%284t%2Bhighlight%287%29%29%284t%2Bhighlight%287%29%29 Multiply the Last terms:%287%29%287%29=49.


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So we have the terms: 16t%5E2, 28t, 28t, 49


16t%5E2%2B28t%2B28t%2B49 Now add every term listed above to make a single expression.


16t%5E2%2B56t%2B49 Now combine like terms.


So %284t%2B7%29%5E2 FOILs to 16t%5E2%2B56t%2B49.


In other words, %284t%2B7%29%5E2=16t%5E2%2B56t%2B49.