Explications étape par étape:

S1 = (2x+1)(2x+1) = (2x+1)² identité remarquable:

S1 = (2x)² + (2×2x×1) + 1² = 4x² + 4x + 1

S2 = (2x+1) × x = 2x² + x

S3 = (2x + 1)(2x-1) identité remarquable

S3 = (2x)² - 1² = 4x² - 1

S1 + S2 + S3 =

4x² + 4x + 1 + 2x² + x + 4x² - 1 = 10x² + 5x

S4 =

(2x + 1) × 5x = 10x² + 5x

S1 + S2 + S3 = S4