SOLUTION: Expand and if necessary simplify questions: a. (2a-1)^2 b. (x+11)(x-4) c. (2x-3)(4x-7)

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Question 170429: Expand and if necessary simplify questions:
a. (2a-1)^2
b. (x+11)(x-4)
c. (2x-3)(4x-7)
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
I'll do the first two to get you started


# 1




%282a-1%29%5E2 Start with the given expression.


%282a-1%29%282a-1%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%282a%29-1%29%28highlight%282a%29-1%29 Multiply the First terms:%282%2Aa%29%2A%282%2Aa%29=4%2Aa%5E2.


%28highlight%282a%29-1%29%282a%2Bhighlight%28-1%29%29 Multiply the Outer terms:%282%2Aa%29%2A%28-1%29=-2%2Aa.


%282a%2Bhighlight%28-1%29%29%28highlight%282a%29-1%29 Multiply the Inner terms:%28-1%29%2A%282%2Aa%29=-2%2Aa.


%282a%2Bhighlight%28-1%29%29%282a%2Bhighlight%28-1%29%29 Multiply the Last terms:%28-1%29%2A%28-1%29=1.


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4%2Aa%5E2-2%2Aa-2%2Aa%2B1 Now collect every term to make a single expression.


4%2Aa%5E2-4%2Aa%2B1 Now combine like terms.


So %282a-1%29%5E2 FOILs to 4%2Aa%5E2-4%2Aa%2B1.


In other words, %282a-1%29%5E2=4a%5E2-4a%2B1.





# 2




%28x%2B11%29%28x-4%29 Start with the given expression.


Now let's FOIL the expression.


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


%28highlight%28x%29%2B11%29%28highlight%28x%29-4%29 Multiply the First terms:%28x%29%2A%28x%29=x%5E2.


%28highlight%28x%29%2B11%29%28x%2Bhighlight%28-4%29%29 Multiply the Outer terms:%28x%29%2A%28-4%29=-4%2Ax.


%28x%2Bhighlight%2811%29%29%28highlight%28x%29-4%29 Multiply the Inner terms:%2811%29%2A%28x%29=11%2Ax.


%28x%2Bhighlight%2811%29%29%28x%2Bhighlight%28-4%29%29 Multiply the Last terms:%2811%29%2A%28-4%29=-44.


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x%5E2-4%2Ax%2B11%2Ax-44 Now collect every term to make a single expression.


x%5E2%2B7%2Ax-44 Now combine like terms.


So %28x%2B11%29%28x-4%29 FOILs to x%5E2%2B7%2Ax-44.


In other words, %28x%2B11%29%28x-4%29=x%5E2%2B7%2Ax-44.