a(b + c) = ab + ac. This can be visualized geometrically as splitting a grid of a rows and (b + c) columns into two smaller grids.a(b + 1) = ab + a.a + b + 1: (a + 1)(b + 1) = ab + a + b + 1.(a + 1)(b - 1) = ab + b - a - 1.(a + m)(b + n) = ab + mb + an + mn. Geometrically, this represents the total area of a grid divided into four distinct sub-regions.(a + b)2 = a2 + 2ab + b2.(a - b)2 = a2 - 2ab + b2.(a + b)(a - b) = a2 - b2.a2 = (a + b)(a - b) + b2 (e.g., 312 = (32 × 30) + 12 = 961).-3p(-5p + 2q) is often mistakenly written as -3p + 5p - 2q. The correct expansion is 15p2 - 6pq.(5m + 6n)2 is NOT equal to 25m2 + 36n2. The middle term 2ab must be included: 25m2 + 60mn + 36n2.5w2 + 6w cannot be simplified to 11w2).(k + 1)2 - 1, k2 + 2k, or k(k + 2)), all simplifying to the same equivalent expression.| Identity Type | Formula |
|---|---|
| General Product | (a + b)(c + d) = ac + ad + bc + bd |
| Square of Sum (Identity 1A) | (a + b)2 = a2 + 2ab + b2 |
| Square of Difference (Identity 1B) | (a - b)2 = a2 - 2ab + b2 |
| Difference of Squares (Identity 1C) | (a + b)(a - b) = a2 - b2 |