mono_poly.md

@@ -208,7 +208,8 @@ Réduire et ordonner les expressions algébriques ci-dessous.
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 6. $\quad 2ab^3 + a^3b - (5aa + 3a^3b - ab^3) =$
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-7. $\quad 5x^3 - 2x + 3x^2 - x^3 + 4x - x^2 + 1 =$
+7. $\quad \dfrac{3}{2}x^2y - \dfrac{1}{2}x^2y + xy^2 - 2xy^2 + \dfrac{4}{3}z - \dfrac{1}{3}z + 5 - 2 =$
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@@ -217,7 +218,7 @@ Réduire et ordonner les expressions algébriques ci-dessous.
 
 1. $\quad 4x^2y \cdot (-3xy^2) \cdot 2y = (4 \cdot (-3) \cdot 2) \cdot x^{2+1} \cdot y^{1+2+1} = \boxed{-24x^3y^4}$
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-2. $\quad \dfrac{3a^2b}{2} \cdot \dfrac{4ab^3}{5} = \dfrac{3 \cdot 4 \cdot a^{2+1} \cdot b^{1+3}}{2 \cdot 5} = \dfrac{12a^3b^4}{10} = \boxed{\dfrac{6a^3b^4}{5}}$
+2. $\quad \dfrac{3a^2b}{2} \cdot \dfrac{4ab^3}{5} = \dfrac{3 \cdot 4 \cdot a^{2+1} \cdot b^{1+3}}{2 \cdot 5} = \dfrac{12a^3b^4}{10} = \boxed{\dfrac{6a^3b^4}{5}}$ ou $\boxed{\dfrac{6}{5}a^3b^4}$
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 3. $\quad (2x^2y)^3 \cdot (-xy^2) = 2^3x^6y^3 \cdot (-xy^2) = 8x^6y^3 \cdot (-xy^2) = \boxed{-8x^7y^5}$
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@@ -225,9 +226,9 @@ Réduire et ordonner les expressions algébriques ci-dessous.
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 5. $\quad 3x^2 + 2xy - x^2 + 5xy - 2y^2 + x^2 = (3-1+1)x^2 + (2+5)xy - 2y^2 = \boxed {3x^2 + 7xy - 2y^2}$
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-6. $\quad 2ab^3 + a^3b - (5aa + 3a^3b - ab^3) = 2ab^3 + a^3b - 5a^2 -3a^3b + ab^3 = (2+1)ab^3 + (1-3)a^3b - 5a^2 = 3ab^3 - 2a^3b - 5a^2 = \boxed{2a^3b - 5a^2 + 3ab^3}$
+6. $\quad 2ab^3 + a^3b - (5aa + 3a^3b - ab^3) = 2ab^3 + a^3b - 5a^2 -3a^3b + ab^3 = (2+1)ab^3 + (1-3)a^3b - 5a^2 = 3ab^3 - 2a^3b - 5a^2 = \boxed{-2a^3b - 5a^2 + 3ab^3}$
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-7. $5x^3 - 2x + 3x^2 - x^3 + 4x - x^2 + 1 = (5-1)x^3 + (3-1)x^2 + (-2+4)x + 1 = \boxed{4x^3 + 2x^2 + 2x + 1}$
+7. $\quad \dfrac{3}{2}x^2y - \dfrac{1}{2}x^2y + xy^2 - 2xy^2 + \dfrac{4}{3}z - \dfrac{1}{3}z + 5 - 2 = \left(\dfrac{3}{2} - \dfrac{1}{2}\right)x^2y + (1 - 2)xy^2 + \left(\dfrac{4}{3} - \dfrac{1}{3}\right)z + (5 - 2) = \boxed{x^2y - xy^2 + z + 3}$
 
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