( x - 5 ) ( x - 8 )
I need someone to explain in words step by step how to get this
i googled the FOIL method and i still dont understand how you get ^2 ect
Thank you in advance i really need it
I need help with algebra?
2008-05-23 3:23 pm
回答 (9)
2008-05-23 3:28 pm
✔ 最佳答案
There several ways of handling these. I will demonstrate the FOIL method.(F)irst Terms: x*x = x²
(O)uter Terms: -8*x = -8x
(I)nner Terms: -5*x = -5x
(L)ast Terms: -5*-8 = 40
Sum of Terms: x² - 8x - 5x + 40
= x² - 13x + 40
I never heard of FOIL until I started teaching. Go Figure!
Add on: (May 23, 08 Time: 10:37AM EST)
------
Here is another way of doing this problem:
http://www.scs.gmu.edu/~mwester1/solution1.pdf
參考: LZY8
2008-05-23 10:50 pm
(x - 5)(x - 8)
= x*x - 5*x - x*8 + 5*8
= x^2 - 5x - 8x + 40
= x^2 - 13x + 40
= x*x - 5*x - x*8 + 5*8
= x^2 - 5x - 8x + 40
= x^2 - 13x + 40
2008-05-23 10:38 pm
FOIL is a memory crutch/reminder to make sure you do ALL the feasible multiplications when multiplying one binomial by another.
There are 4 possible multiplications (a 2-term times a 2-term yields 4 product terms). Were you multiplying a trinomial times a trinomial you would have 9 multiplications. When the multiplications get lengthier (like the trinomial times a trinomial) sometimes doing the multiplication like conventional multiplication will help you keep the like/similar terms column-grouped together; that makes combining/collecting them easier.
There are 4 possible multiplications (a 2-term times a 2-term yields 4 product terms). Were you multiplying a trinomial times a trinomial you would have 9 multiplications. When the multiplications get lengthier (like the trinomial times a trinomial) sometimes doing the multiplication like conventional multiplication will help you keep the like/similar terms column-grouped together; that makes combining/collecting them easier.
2008-05-23 10:33 pm
FOIL means First, Outer, Inner , Last
refers to the order in which you multiply the terms of binomials.
So FIRST --
in your example (x-5) (x-8)
the First terms are the 2 Xs
so X*X = X^2 (x squared)
now - OUTER
the 2 outer terms are the x from the 1st binomial and the -8 from the 2nd binomial
multiply them together and you get -8x
INNER : multiply the 2 inner terms (-5) * (x)
and you get -5x
Finally : LAST - you multiply the Last terms of each binomial
in this case it would be (-5)*(-8)
= 40
Now you simply add them all up
x^2 -8x -5x + 40 (ok?)
Now you can simplify by combining like terms - the Xs
-8x-5x = - 13x
so x^2-13x+40 is your final answer
refers to the order in which you multiply the terms of binomials.
So FIRST --
in your example (x-5) (x-8)
the First terms are the 2 Xs
so X*X = X^2 (x squared)
now - OUTER
the 2 outer terms are the x from the 1st binomial and the -8 from the 2nd binomial
multiply them together and you get -8x
INNER : multiply the 2 inner terms (-5) * (x)
and you get -5x
Finally : LAST - you multiply the Last terms of each binomial
in this case it would be (-5)*(-8)
= 40
Now you simply add them all up
x^2 -8x -5x + 40 (ok?)
Now you can simplify by combining like terms - the Xs
-8x-5x = - 13x
so x^2-13x+40 is your final answer
2008-05-23 10:32 pm
first outer inner last
(x - 5)(x - 8)
take the two first digits in the brackets: x multiplyed by x is x^2
outer: the first x and the last 8
x multiplyed by NEGATIVE8 = NEGATIVE8x (-8x)
inner: the NEGATIVE5 multiplyed by the second x
-5 multiplyed by x = NEGATIVE5x (-5x)
last: NEGATIVE5 multiplyed by NEGATIVE8 = POSITIVE40
add all the same values together- as in all the ^2, all the ^1 and the numbers
x^2 + (-5x + (-8x)) + 40
= x^2 -13x + 40
simple :)
(x - 5)(x - 8)
take the two first digits in the brackets: x multiplyed by x is x^2
outer: the first x and the last 8
x multiplyed by NEGATIVE8 = NEGATIVE8x (-8x)
inner: the NEGATIVE5 multiplyed by the second x
-5 multiplyed by x = NEGATIVE5x (-5x)
last: NEGATIVE5 multiplyed by NEGATIVE8 = POSITIVE40
add all the same values together- as in all the ^2, all the ^1 and the numbers
x^2 + (-5x + (-8x)) + 40
= x^2 -13x + 40
simple :)
2008-05-23 10:28 pm
Foil...
First two terms: x * x = x^2
Outer two terms: x * (-8) = -8x
Inner two terms: (-5) * x = -5x
Last two terms: (-5)(-8) = 40
(x-5)(x-8) = x^2 - 13x +40
First two terms: x * x = x^2
Outer two terms: x * (-8) = -8x
Inner two terms: (-5) * x = -5x
Last two terms: (-5)(-8) = 40
(x-5)(x-8) = x^2 - 13x +40
2008-05-23 10:27 pm
it the distrubitive proptery
2008-05-23 10:43 pm
How old are you? ;)
2008-05-23 10:29 pm
FOIL: First, Outer, Inner, Last
( x - 5 ) ( x - 8 )
The first term of (x-5) is x
The last term of (x-5) is 5
The first term of (x-8) is x
The last term of (x-8) is 8
Outer terms are the ones on the ends.
(x from x-5, and -8 from x -8)
Inner terms are the ones in the middle.
( -5 from x-5, and x from x-8)
The FIRST terms multiplied together:
x * x = (x)(x) = x²
The OUTER terms multiplied together:
x * (-8) = -8x
The INNER terms multiplied together:
(-5) * x = -5x
The LAST terms multiplied together:
(-5) * (-8) = 40
Add them all up:
x² - 8x - 5x + 40
x² - 13x + 50
So, you end up with
( x - 5 ) ( x - 8 ) = x² - 13x + 50
( x - 5 ) ( x - 8 )
The first term of (x-5) is x
The last term of (x-5) is 5
The first term of (x-8) is x
The last term of (x-8) is 8
Outer terms are the ones on the ends.
(x from x-5, and -8 from x -8)
Inner terms are the ones in the middle.
( -5 from x-5, and x from x-8)
The FIRST terms multiplied together:
x * x = (x)(x) = x²
The OUTER terms multiplied together:
x * (-8) = -8x
The INNER terms multiplied together:
(-5) * x = -5x
The LAST terms multiplied together:
(-5) * (-8) = 40
Add them all up:
x² - 8x - 5x + 40
x² - 13x + 50
So, you end up with
( x - 5 ) ( x - 8 ) = x² - 13x + 50
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