Question

A² + b² = 7b and b² + (2b-a)² = 7² find (a - b)².

Answer 1

Answer:

(a - b)^2 = 49 - 4b^2 +2ab

Step-by-step 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