(A*x + B*x^2 + C)*(E*x + F)
just plug and chug
AEx^2 + BEx^3 + CEx
+ AFx + BFx^2 + CF
now add 'em up
(A*x + B*x^2 + C)*(E*x + F)
A*x (E*x) + A*x(F) + B*x^2(E*x )+ B*x^2(F)+C(E*x )+ C(F)
To simplify the given expression (A*x + B*x^2 + C)*(E*x + F), we can use the distributive property of multiplication over addition. This means that we need to multiply each term in the first set of parentheses by each term in the second set of parentheses, and then combine like terms.
Let's break it down step by step:
1. Multiply the first term in the first set of parentheses, A*x, by each term in the second set of parentheses, E*x and F:
(A*x)*(E*x) = A*E*x^2,
(A*x)*F = A*F*x.
2. Multiply the second term in the first set of parentheses, B*x^2, by each term in the second set of parentheses, E*x and F:
(B*x^2)*(E*x) = B*E*x^3,
(B*x^2)*F = B*F*x^2.
3. Multiply the last term in the first set of parentheses, C, by each term in the second set of parentheses, E*x and F:
C*(E*x) = C*E*x,
C*F = C*F.
4. Combine all the terms obtained in the previous steps:
A*E*x^2 + A*F*x + B*E*x^3 + B*F*x^2 + C*E*x + C*F.
The final result of simplifying the given expression is:
A*E*x^2 + A*F*x + B*E*x^3 + B*F*x^2 + C*E*x + C*F.