mono_poly.md

@@ -193,41 +193,41 @@ Pour multiplier des monômes :
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 ## :yellow_circle: Niveau B - attendu pour débuter des études ES
-
+Réduire et ordonner les expressions algébriques ci-dessous.
 >>>
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-1. Réduire et ordonner : $4x^2y \cdot (-3xy^2) \cdot 2y =$
+1. $\quad 4x^2y \cdot (-3xy^2) \cdot 2y =$
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-2. Réduire et ordonner : $\dfrac{3a^2b}{2} \cdot \dfrac{4ab^3}{5} =$
+2. $\quad \dfrac{3a^2b}{2} \cdot \dfrac{4ab^3}{5} =$
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-3. Réduire et ordonner : $(2x^2y)^3 \cdot (-xy^2) =$
+3. $\quad (2x^2y)^3 \cdot (-xy^2) =$
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-4. Réduire et ordonner : $\dfrac{6x^3y^2}{2xy} \cdot \dfrac{4xy^3}{3x^2} =$
+4. $\quad \dfrac{6x^3y^2}{2xy} \cdot \dfrac{4xy^3}{3x^2} =$
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-5. Réduire et ordonner : $3x^2 + 2xy - x^2 + 5xy - 2y^2 + x^2 =$
+5. $\quad 3x^2 + 2xy - x^2 + 5xy - 2y^2 + x^2 =$
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-6. Réduire et ordonner : $2ab^3 + a^3b - (5aa + 3a^3b - ab^3) =$
+6. $\quad 2ab^3 + a^3b - (5aa + 3a^3b - ab^3) =$
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-7. Réduire et ordonner : $5x^3 - 2x + 3x^2 - x^3 + 4x - x^2 + 1 =$
+7. $\quad 5x^3 - 2x + 3x^2 - x^3 + 4x - x^2 + 1 =$
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 >>>
 
 <details>
 <summary>:check_mark_button: Solutions Niveau B</summary>
 
-1. $4x^2y \cdot (-3xy^2) \cdot 2y = (4 \cdot (-3) \cdot 2) \cdot x^{2+1} \cdot y^{1+2+1} = -24x^3y^4$
+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. $\dfrac{3a^2b}{2} \cdot \dfrac{4ab^3}{5} = \dfrac{3 \cdot 4 \cdot a^{2+1} \cdot b^{1+3}}{2 \cdot 5} = \dfrac{12a^3b^4}{10} = \dfrac{6a^3b^4}{5}$
+2. $\quad \dfrac{3a^2b}{2} \cdot \dfrac{4ab^3}{5} = \dfrac{3 \cdot 4 \cdot a^{2+1} \cdot b^{1+3}}{2 \cdot 5} = \dfrac{12a^3b^4}{10} = \boxed{\dfrac{6a^3b^4}{5}}$
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-3. $(2x^2y)^3 \cdot (-xy^2) = 2^3x^6y^3 \cdot (-xy^2) = 8x^6y^3 \cdot (-xy^2) = -8x^7y^5$
+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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-4. $\dfrac{6x^3y^2}{2xy} \cdot \dfrac{4xy^3}{3x^2} = \dfrac{6x^3y^2 \cdot 4xy^3}{2xy \cdot 3x^2} = \dfrac{24x^4y^5}{6x^3y} = 4xy^4$
+4. $\quad \dfrac{6x^3y^2}{2xy} \cdot \dfrac{4xy^3}{3x^2} = \dfrac{6x^3y^2 \cdot 4xy^3}{2xy \cdot 3x^2} = \dfrac{24x^4y^5}{6x^3y} = \boxed {4xy^4}$
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-5. $3x^2 + 2xy - x^2 + 5xy - 2y^2 + x^2 = (3-1+1)x^2 + (2+5)xy - 2y^2 = 3x^2 + 7xy - 2y^2$
+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. $2ab^3 + a^3b - (5aa + 3a^3b - ab^3) = 2ab^3 + a^3b - 5a^2 -3a^3b + ab^3 = (2+1)ab^3 + (1-3)a^3b - 5a^2 = 3ab^3 - 2a^3b - 5a^2 = \boxed{2a^3b - 5a^2 + 3ab^3}$
+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. $5x^3 - 2x + 3x^2 - x^3 + 4x - x^2 + 1 = (5-1)x^3 + (3-1)x^2 + (-2+4)x + 1 = 4x^3 + 2x^2 + 2x + 1$
+7. $5x^3 - 2x + 3x^2 - x^3 + 4x - x^2 + 1 = (5-1)x^3 + (3-1)x^2 + (-2+4)x + 1 = \boxed{4x^3 + 2x^2 + 2x + 1}$
 
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