MATH LESSON PRODUCT OF SUM & DIFFERENCE When multiplying a sum and difference of the same two terms, the middle terms cancel! When multiplying a sum and difference of the same two terms, the middle terms cancel, leaving a difference of squares. (a + b)(a − b) = a² − b² (a + b) × (a − b) = a² − b² Understanding the Pattern When you multiply (a + b) by (a − b) , the result has only 2 terms — NOT 3! The middle terms cancel each other out because they are opposites . 1st term: a² — first term squared 2nd term: − b² — second term squared , always negative NO middle term! It cancelled out! Why Do the Middle Terms Cancel? Use FOIL on (a + b)(a − b) and watch what happens: (a + b)(a − b) F: a · a = a² O: a · (−b) = −ab I: b · a = +ab L: b · (−b) = −b² O + I: −ab + +ab = 0 (CANCELE...
MATH LESSON SQUARE OF A DIFFERENCE Master the formula: (a − b)² = a² − 2ab + b² (a − b)² = a² − 2ab + b² Understanding the Formula The square of a difference means you multiply (a − b) by itself . The result is a perfect square trinomial with 3 terms: 1st term: a² — square the first term 2nd term: −2ab — multiply both, double it, make it negative 3rd term: +b² — square the second term (always positive ) Where Does −2ab Come From? When you use FOIL on (a − b)(a − b) , the Outer and Inner products are both −ab . Adding them gives −2ab ! (a − b)(a − b) F: a · a = a² O: a · (−b) = −ab I: (−b) · a = −ab L: (−b) · (−b) = +b² Combine O + I: −ab + (−ab) = −2ab Final: a² − 2ab + b² Common Mistakes! Mistake 1: Forg...