Question

Desarrolla, opera y simplifica

a) (5x² + 2x) . (5x² - 2x) - (5x² - 2x)²

b) (a + b)² - (a - b)² + (a + b) . (a - b)

Answer 1

(5x² + 2x) . (5x² - 2x) - (5x² - 2x)²
[(5x²) (5x²) + (5x²) (- 2x) + (2x) (5x²) + (2x) (- 2x)] - (25x⁴ - 20x³ + 4x²)
[(25x⁴) + (- 10x³) + (10x³) + (- 4x²)] - 25x⁴ + 30x³ - 4x²
[25x⁴ - 10x³ + 10x³ - 4x²] - 25x⁴ + 20x³ - 4x²
[25x⁴ - 4x²] - 25x⁴ + 20x³ - 4x²
25x⁴ - 4x² - 25x⁴ + 20x³ - 4x²
25x⁴ - 25x⁴ + 20x³ - 4x² - 4x²
20x³ - 8x²
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(a + b)² - (a - b)² + (a + b) . (a - b)
[(a)² - 2(a * b) + (b)² - (a²) - 2 (a * b) + (- b)² + [(a) (a) + (a) (- b) + (b) (a) + (b) (- b)]
[(a²) + 2 (ab) + b² - a² + 2 (ab) + b² + [a² - ab + ab - b²]
[a² + 2ab + b² - a² + 2ab + b² + [a² - b²]
[a² - a² + 2ab + 2ab + b² + b²] + a² - b²
[4ab + 2b²] + a² - b²
4ab + 2b² + a² - b²
a² + 4ab + b²