SOLUTION: Simplify the expression: ( 4 x + 1 ) 2 + (2 x - 4 ) 2 Choose the correct answer from the following: 20x 2 - 8x + 17 12x 2 - 8x + 15 4x 2 + 8x - 15

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: Simplify the expression: ( 4 x + 1 ) 2 + (2 x - 4 ) 2 Choose the correct answer from the following: 20x 2 - 8x + 17 12x 2 - 8x + 15 4x 2 + 8x - 15      Log On


   

Question 145203: Simplify the expression:
( 4 x + 1 ) 2 + (2 x - 4 ) 2
Choose the correct answer from the following:
20x 2 - 8x + 17
12x 2 - 8x + 15
4x 2 + 8x - 15
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
First FOIL %28+4+x+%2B+1+%29+%5E+2

%282x-4%29%5E2 Start with the given expression


%284x%2B1%29%284x%2B1%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%284x%29%2B1%29%28highlight%284x%29%2B1%29 Multiply the First terms:%284x%29%2A%284x%29=16x%5E2


%28highlight%284x%29%2B1%29%284x%2Bhighlight%281%29%29 Multiply the Outer terms:%284x%29%2A%281%29=4x


%284x%2Bhighlight%281%29%29%28highlight%284x%29%2B1%29 Multiply the Inner terms:%281%29%2A%284x%29=4x


%284x%2Bhighlight%281%29%29%284x%2Bhighlight%281%29%29 Multiply the Last terms:%281%29%2A%281%29=1


16x%5E2%2B4x%2B4x%2B1 Now collect every term to make a single expression



16x%5E2%2B8x%2B1 Now combine like terms


So %284x%2B1%29%5E2 foils and simplifies to 16x%5E2%2B8x%2B1

In other words, %284x%2B1%29%5E2=16x%5E2%2B8x%2B1







Now let's FOIL %282+x+-+4+%29%5E+2+



%282x-4%29%282x-4%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%282x%29-4%29%28highlight%282x%29-4%29 Multiply the First terms:%282x%29%2A%282x%29=4x%5E2


%28highlight%282x%29-4%29%282x%2Bhighlight%28-4%29%29 Multiply the Outer terms:%282x%29%2A%28-4%29=-8x


%282x%2Bhighlight%28-4%29%29%28highlight%282x%29-4%29 Multiply the Inner terms:%28-4%29%2A%282x%29=-8x


%282x%2Bhighlight%28-4%29%29%282x%2Bhighlight%28-4%29%29 Multiply the Last terms:%28-4%29%2A%28-4%29=16


4x%5E2-8x-8x%2B16 Now collect every term to make a single expression



4x%5E2-16x%2B16 Now combine like terms


So %282x-4%29%5E2 foils and simplifies to 4x%5E2-16x%2B16

In other words, %282x-4%29%5E2=4x%5E2-16x%2B16






So %28+4+x+%2B+1+%29+%5E+2%2B+%282+x+-+4+%29%5E+2+ now becomes %2816x%5E2%2B8x%2B1%29%2B%284x%5E2-16x%2B16%29


%2816x%5E2%2B8x%2B1%29%2B%284x%5E2-16x%2B16%29 Start with the given expression


20x%5E2-8x%2B17 Combine like terms



So %28+4+x+%2B+1+%29+%5E+2%2B+%282+x+-+4+%29%5E+2=20x%5E2-8x%2B17