Key algebraic identities for multiplication, including square of sum, square of difference, and difference of squares.

- The first identity, (a + b)² = a² + 2ab + b², is derived by expanding the square of a binomial: (a + b)(a + b) = a(a) + a(b) + b(a) + b(b) = a² + ab + ab + b² = a² + 2ab + b².
- The second identity, (a - b)² = a² - 2ab + b², follows similarly: (a - b)(a - b) = a(a) - a(b) - b(a) + b(b) = a² - ab - ab + b² = a² - 2ab + b².
- The third identity, (a + b)(a - b) = a² - b², represents the difference of squares: multiplying the sum and difference of two terms gives the square of the first minus the square of the second.