Answer:
(a - b)^2 = 49 - 4b^2 +2ab
Explanation:
Given: a^2 + b^2 = 7b (assuming A is really “a”)
b^2 + (2b - a)^2 = 7^2
Find; (a - b)^2
Plan: Use Algebraic Manipulation
Start with b^2 + (2b - a)^2 = 7^2 =>
b^2 + 4b^2 - 4ab + a^2 = 49 by expanding the binomial.
a^2 + b^2 + 4b^2 - 4ab = 49 rearranging terms
a^2 + b^2 -2ab - 2ab + 4b^2 = 49 =>
a^2 - 2ab + b^2 = 49 - 4b^2 +2ab rearranging and subtracting 4b^2 and adding 2ab to both sides of the equation and by factoring a^2 - 2ab + b^2
(a - b)^2 = 49 - 4b^2 +2ab
Double Check: recalculated ✅ ✅
(a - b)^2 = 49 - 4b^2 +2ab