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Question 427308: multiply
(x^9+x^8)(x^9+x^8-x^7)=
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! (x^9+x^8)(x^9+x^8-x^7) equals:
(x^9 * ((x^9+x^8-x^7)) + (x^8 * (x^9+x^8-x^7)) equals:
(x^9*x^9) + (x^9*x^8) - (x^9*x^7) + (x^8*x^9) + (x^8*x^8) - (x^8*x^7) equals:
x^18 + x^17 - x^16 + x^17 + x^16 - x^15
reorder the terms to get like terms together:
x^18 + (x^17 + x^17) + (x^16 - x^16) - x^15
combine like terms to get:
x^18 + 2*x^17 - x^15
a quick way to check is to give a value to x and see if the original equation and the final equation come up with the same answer.
use your calculator to do the arithmetic.
assuming that x = 3, then:
original equation of (x^9+x^8)(x^9+x^8-x^7) = (3^9+3^8)(3^9+3^8-3^7) = 631351908
final equation of x^18 + 2*x^17 - x^15 = 3^18 + 2*3^17 - 3^15 = 631351908
looks like we did it right.
the method of multiplication is that each term in the second expression is multiplied by each term in the first expression.
in general, this looks like:
(a + b) * (c + d + e) = a * (c + d + e) + b * (c + d + e) = a*c + a*d + a*e + b*c + b*d + b*e
every term in the second expression has been multiplied by every term in the first expression exactly 1 time.
this could also be shown as:
(c + d + e) * (a + b) = c * (a + b) + d * (a + b) + e * (a + b) = a*c + b*c + a*d + b*d + a*e + b*e.
if you reorder these terms you get:
a*c + a*d + a*e + b*c + b*d + b*e
whether you do it as (a + b) * (c + d + e) or (c + d + e) * (a + b) doesn't matter.
the result is the same.
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