Question 502880: (a+t)(a^2-at+t^2)
Answer by persian52(161)   (Show Source):
You can put this solution on YOUR website! (a+t)(a^(2)-at+t^(2))
Multiply each term in the first polynomial by each term in the second polynomial.
(a*a^(2)+a*-at+a*t^(2)+t*a^(2)+t*-at+t*t^(2))
Multiply a by a^(2) to get a^(3).
(a^(3)+a*-at+a*t^(2)+t*a^(2)+t*-at+t*t^(2))
Multiply a by -at to get -a^(2)t.
(a^(3)-a^(2)t+a*t^(2)+t*a^(2)+t*-at+t*t^(2))
Multiply a by t^(2) to get at^(2).
(a^(3)-a^(2)t+at^(2)+t*a^(2)+t*-at+t*t^(2))
Multiply t by a^(2) to get a^(2)t.
(a^(3)-a^(2)t+at^(2)+a^(2)t+t*-at+t*t^(2))
Multiply t by -at to get -at^(2).
(a^(3)-a^(2)t+at^(2)+a^(2)t-at^(2)+t*t^(2))
Multiply t by t^(2) to get t^(3).
(a^(3)-a^(2)t+at^(2)+a^(2)t-at^(2)+t^(3))
According to the distributive property, for any numbers a, b, and c, a(b+c)=ab+ac and (b+c)a=ba+ca. Here, a^(2)t is a factor of both -a^(2)t and a^(2)t.
(a^(3)+(-1+1)a^(2)t+at^(2)-at^(2)+t^(3))
To add integers with different signs, subtract their absolute values and give the result the same sign as the integer with the greater absolute value. In this example, subtract the absolute values of -1 and 1 and give the result the same sign as the integer with the greater absolute value.
(a^(3)+(0)a^(2)t+at^(2)-at^(2)+t^(3))
Remove the parentheses.
(a^(3)+at^(2)-at^(2)+t^(3))
According to the distributive property, for any numbers a, b, and c, a(b+c)=ab+ac and (b+c)a=ba+ca. Here, at^(2) is a factor of both at^(2) and -at^(2).
(a^(3)+(1-1)at^(2)+t^(3))
To add integers with different signs, subtract their absolute values and give the result the same sign as the integer with the greater absolute value. In this example, subtract the absolute values of 1 and -1 and give the result the same sign as the integer with the greater absolute value.
(a^(3)+(0)at^(2)+t^(3))
Remove the parentheses.
(a^(3)+t^(3))
Remove the parentheses around the expression a^(3)+t^(3).
a^(3)+t^(3)
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