Question

Rozłóż wyrażenianaczynniki stosując wzory skróconego mnożenia.

(m-9n)kwadrat-9mkwadrat
a kwadrat - (x+y) kwadrat =
4-(2a-3b)kwadrat =
(2x+3)kwadrat - (x-1)kwadrat =
4(a-b)kwadrat - (a + b)kwadrat =

Answer 1

(m-9n)² - 9m² = m² - 2×m×9n + 81n² - 9m² = -8m² - 18mn + 81n²

a² - (x+y)² = a² - (x² + 2×x×y + y²) = a² - x² - 2xy - y²

4 - (2a - 3b)² = 4 - 4a² - 2×2a×3b + 9b² = 4 - 4a² + 12ab - 9b² =

(2x+3)² - (x-1)² = 4x² + 2×2x×3 + 9 - (x² - 2×x×1 + 1) = 4x² + 12x + 9 - x² + 2x - 1 = 3x² + 14x +8

4 (a - b)² - (a + b)² = 4 (a² - 2ab + b²) - (a² + 2ab + b²) = 4a² - 8ab + 4b² - a² - 2ab - b² = 3a² - 10ab + 3b²

Answer 2

1) (mkwadrat - 18mn + 81nkwadrat) - 9 mkwadrat = -8mkwadrat - 18mn +81nkwadrat

2) akwadrat - (xkwadrat + 2xy + ykwadrat) = akawdrat - xkwadrat - 2xy - ykwadrat

3) 4 - (2a - 3b)kwadrat = 4 - (4akwadrat - 12ab + 9bkwadrat) = 4 - 4akwadrat + 12ab - 9 bkwadrat

4) 4xkwadrat + 12x +9 - (xkwadrat - 2x +1) + 4xkwadrat + 12x+9 -xkwadrat + 2x -1 = 3xkwadrat +14x + 8

5) akwadrat - 2ab + bkwadrat - (akwadrat + 2ab + bkwadrat) = akwadrat - 2ab + bkwadrat - akwadrat - 2ab - bkwadrat = -4ab

Answer 3

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