SOLUTION: find each product: 1.(3y-1)(2y+7) 2. (4x-5)(2x+9) 3. (y-3)(y-3)

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: find each product: 1.(3y-1)(2y+7) 2. (4x-5)(2x+9) 3. (y-3)(y-3)      Log On


   

Question 88875: find each product:
1.(3y-1)(2y+7)
2. (4x-5)(2x+9)
3. (y-3)(y-3)
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
1.
Start with the given expression

%283y-1%29%282y%2B7%29

When you FOIL, you multiply the terms in this order:
F-First (i.e. you multiply the first terms in each parenthesis which in this case are 3y and 3y)
O-Outer (i.e. you multiply the outer terms in each parenthesis which in this case are 3y and -1)
I-Inner (i.e. you multiply the inner terms in each parenthesis which in this case are -1 and 3y)
L-Last (i.e. you multiply the last terms in each parenthesis which in this case are -1 and -1)


So lets multiply the first terms:
3y%2A2y=6y%5E2 multiply 3y and 2y to get 6y%5E2



So lets multiply the outer terms:
3y%2A7=21y multiply 3y and 7 to get 21y



So lets multiply the inner terms:
-1%2A2y=-2y multiply -1 and 2y to get -2y



So lets multiply the last terms:
-1%2A7=-7 multiply -1 and 7 to get -7

Now lets put everything together
%283y-1%29%282y%2B7%29=6y%5E2%2B21y-2y-7=6y%5E2%2B19y-7

So the expression

%283y-1%29%282y%2B7%29

FOILs to:

6y%5E2%2B19y-7

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2.
Start with the given expression

%284x-5%29%282x%2B9%29

When you FOIL, you multiply the terms in this order:
F-First (i.e. you multiply the first terms in each parenthesis which in this case are 4x and 4x)
O-Outer (i.e. you multiply the outer terms in each parenthesis which in this case are 4x and -5)
I-Inner (i.e. you multiply the inner terms in each parenthesis which in this case are -5 and 4x)
L-Last (i.e. you multiply the last terms in each parenthesis which in this case are -5 and -5)


So lets multiply the first terms:
4x%2A2x=8x%5E2 multiply 4x and 2x to get 8x%5E2



So lets multiply the outer terms:
4x%2A9=36x multiply 4x and 9 to get 36x



So lets multiply the inner terms:
-5%2A2x=-10x multiply -5 and 2x to get -10x



So lets multiply the last terms:
-5%2A9=-45 multiply -5 and 9 to get -45

Now lets put everything together
%284x-5%29%282x%2B9%29=8x%5E2%2B36x-10x-45=8x%5E2%2B26x-45

So the expression

%284x-5%29%282x%2B9%29

FOILs to:

8x%5E2%2B26x-45

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3.
Start with the given expression

%28y-3%29%28y-3%29

When you FOIL, you multiply the terms in this order:
F-First (i.e. you multiply the first terms in each parenthesis which in this case are y and y)
O-Outer (i.e. you multiply the outer terms in each parenthesis which in this case are y and -3)
I-Inner (i.e. you multiply the inner terms in each parenthesis which in this case are -3 and y)
L-Last (i.e. you multiply the last terms in each parenthesis which in this case are -3 and -3)


So lets multiply the first terms:
y%2Ay=y%5E2 multiply y and y to get y%5E2



So lets multiply the outer terms:
y%2A-3=-3y multiply y and -3 to get -3y



So lets multiply the inner terms:
-3%2Ay=-3y multiply -3 and y to get -3y



So lets multiply the last terms:
-3%2A-3=9 multiply -3 and -3 to get 9

Now lets put everything together
%28y-3%29%28y-3%29=y%5E2-3y-3y%2B9=y%5E2-6y%2B9

So the expression

%28y-3%29%28y-3%29

FOILs to:

y%5E2-6y%2B9

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