Question 425972
3a squared would be shown as 3a^2


the ^ is exponent symbol.


your problem is (a+2) * (3a^2 - a + 5)


in polynomial multiplication, every element in the each factor is multiplied by every element in each other factor.


your problem is equivalent to:


(a * (3a^2 - a + 5)) + (2 * (3a^2 - a + 5))


this gets you:


3a^3 - a^2 + 5a + 6a^2 - 2a + 10


combine like terms to get:


3a^3 + 5a^2 + 3a + 10


this works with any number of factors.


you can use it in place of foil.


(a + 2) * (a - 2) = a * (a - 2) + 2 * (a - 2) = a^2 - 2a + 2a + 4 = a^2 + 4


the general form of this would be:


(a + b) * (c + d) = a * (c + d) + b * (c + d)


in your problem, the general form would be:


(a + b) * (c + d + e) = a * (c + d + e) + b * (c + d + e)