Factoring (a + b)^2  a^2 + b^2
This article will guide you through the process of factoring the expression (a + b)^2  a^2 + b^2.
Understanding the Expression
The expression involves squaring a binomial, subtracting a squared term, and adding another squared term. Let's break it down:
 (a + b)^2: This is a binomial squared, which expands to a^2 + 2ab + b^2 using the formula (x + y)^2 = x^2 + 2xy + y^2.
  a^2: This is a simple squared term.
 + b^2: This is another simple squared term.
The Factorization Process

Expand the binomial: Begin by expanding the squared term:
(a + b)^2  a^2 + b^2 = (a^2 + 2ab + b^2)  a^2 + b^2

Simplify by combining like terms:
(a^2 + 2ab + b^2)  a^2 + b^2 = 2ab + 2b^2

Factor out the common factor: Notice that both terms in the expression have 2b in common. Factor it out:
2ab + 2b^2 = 2b(a + b)
Final Result
Therefore, the factored form of the expression (a + b)^2  a^2 + b^2 is 2b(a + b).