Question

Subtract 3a(a + b + c) – 2b(a – b + c) from 4c(–a + b + c).

A) c(11a + 7b - 7c)
B) c(7a - 11b + 7c)
C) c(7a + 11b - 7c)
D) c(11a - 7b + 7c)

Answer 1

To subtract the given algebraic expressions, each expression is first expanded, the appropriate terms are subtracted from the third expression, like terms are combined, and c is factored out to get the final result. There seems to be a mismatch between the coefficients in the final simplified expression and the answer choices provided.

Step-by-step explanation:

The student is asking to subtract multiple algebraic expressions and simplify the result. The expressions involve a combination of multiplication and addition within parentheses, followed by distribution of a variable factor.

Let's approach the problem step by step:

1. First, expand each of the expressions:
   3a(a + b + c) = 3a² + 3ab + 3ac
   2b(a - b + c) = 2ab - 2b² + 2bc
   4c(-a + b + c) = -4ac + 4bc + 4c²
2. Now subtract the first two expressions from the third one:
   -4ac + 4bc + 4c² - (3a² + 3ab + 3ac) + (2ab - 2b² + 2bc)
3. Simplify the result:
   -4ac + 4bc + 4c² - 3a² - 3ab - 3ac + 2ab - 2b² + 2bc
   Combine like terms:
   -3a² + (-4ac - 3ac) + (4bc + 2bc) + 4c² + (2ab - 3ab) - 2b²
   Result: -3a² - 7ac + 6bc + 4c² - ab - 2b²
4. Factor out c from the terms with c to arrive at the final simplified expression. Note that since the coefficients in this final expression do not match any of the answer choices provided, there may be an error in the provided answer choices or in the problem setup that was posed to us.