The textbook introduces several algebraic identities for factorization. For expressions with three squared terms and three cross terms, we use the identity (x + y + z)^2 = $x^{2}$ + $y^{2}$ + $z^{2}$ + 2xy + 2xz + 2yz, carefully determining the signs of x, y, and z from the cross terms. For perfect square trinomials, we apply (a + b)^2 = $a^{2}$ + 2ab + $b^{2}$ or (a - b)^2 = $a^{2}$ - 2ab + $b^{2}$. For quadratic trinomials of the form $x^{2}$ + (a+b)x + ab, we find two numbers that multiply to the constant term and add to the coefficient of the middle term, factoring as (x + a)(x + b).