Final answer:
The coefficient A in the expression (x-3)(x²+7x+7), which represents the x³ term, is found by multiplying the x term from the first binomial with the x² from the second binomial, resulting in A equalling 1.
Step-by-step explanation:
The expression (x-3)(x²+7x+7) equals Ax³+Bx²+Cx+D where A equals the coefficient of the x cubed term, which is derived from the expansion of the given expression. To find A, we focus on the multiplication of the x terms that will contribute to the x³ term. We only need to consider the x and x² terms since they are the only ones that will give us x³ when multiplied together.
Multiplying the x from the first binomial and the x² from the second binomial gives us x³. Since there are no other terms that will produce an x³ term upon multiplication, we can determine that A = 1. Hence, the coefficient of x cubed, or A, in the expanded form of (x-3)(x²+7x+7) is 1.