Doprowadź do najprostszej postaci:
a) (10x + 3y)² - (2y - 5x)²=
b) (6a + 1)² + 2·(3a - 4)²=
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a)
(10x + 3y)² - (2y - 5x)² = (10x)² + 2 · 10x · 3y + (3y)² - [(2y)² - 2 · 2y · 5x + (5x)²] =
= 100x² + 60xy + 9y² - ( 4y² - 20xy + 25x² ) =
= 100x² + 60xy + 9y² - 4y² + 20xy - 25x² =
= 75x² + 80xy + 5y²
b)
(6a + 1)² + 2 · (3a - 4)² = (6a)² + 2 · 6a · 1 + 1² + 2 · [ (3a)² - 2 · 3a · 4 + 4² ] =
= 36a² + 12a + 1 + 2 · ( 9a² - 24a + 16 ) =
= 36a² + 12a + 1 + 18a² - 48a + 32 =
= 54a² - 36a + 33