Vediamo ora alcuni esempi di espressioni con i monomi:
- Esempio 1: \( -[-a (-2b)^3 (-a)^2]^2 + (-2ab)^6 = \)
Semplifichiamo l’espressione, mettendo in pratica tutte le regole che abbiamo visto precedentemente:
\( – [ -a (-2)^3 (b)^3 a^2]^2 + (-2)^6 a^6 b^6 = \)
\( – [-a (-8) b^3 a^2]^2 + 64 a^6 b^6 = \)
\( – [8a b^3 a^2]^2 + 64 a^6 b^6 = \)
\( -[8a^{1+2} b^3]^2 + 64 a^6 b^6 = \)
\( -8^2 (a^{3\times 2}) (b^{3\times 2}) + 64 a^6 b^6 = \)
\( -64 a^6 b^6 + 64 a^6 b^6 = 0 \)
- Esempio 2:
\( \big\{[- (-x)^2]^2 \times \frac{1}{2} x^3\big\}^4 + \frac{1}{4} x^{20} \big(-\frac{1}{4} x^8\big) = \)
\( \big\{[-x^2]^2 \times \frac{1}{2} x^3\big\}^4 + \frac{1}{4} \big(-\frac{1}{4}\big) x^{20} x^8 = \)
\( \big\{x^{2\times 2} \times \frac{1}{2} x^3\big\}^4 – \frac{1}{16} x^{20+8} = \)
\( \big\{\frac{1}{2} x^4 x^3\big\}^4 -\frac{1}{16} x^{28} = \big\{\frac{1}{2} x^{4+3} \big\}^4 – \frac{1}{16} x^{28} = \)
\( \big\{\frac{1}{2} x^7\big\}^4 -\frac{1}{16} x^{28} = \big(\frac{1}{2}\big)^4 (x^7)^4 – \frac{1}{16} x^{28} = \)
\( \frac{1}{16} x^{7 \times 4} – \frac{1}{16} x^{28} = \frac{1}{16} x^{28} – \frac{1}{16} x^{28} = \)
\( \big(\frac{1}{16} – \frac{1}{16}) x^{28} = 0 x^{28} = 0 \)
- Es. 3:
\( [(-xy^3) (-5x^3y) : (-xy)^2]^2 : (-5xy^2)^2 + x^2 – (-2x)^2 = \)
\( [(5x^{1+3} y^{3+1} ) : (x^2 y^2)]^2 : (25x^2 y^4) + x^2 – (4x^2) = \)
\( [(5x^4y^4) : (x^2 y^2)]^2 : (25x^2 y^4) + x^2 – 4x^2 = \)
\( [5x^{4-2} y^{4-2}]^2 : (25x^2 y^4) – 3x^2 = \)
\( [5x^2 y^2]^2 : (25x^2 y^4) – 3x^2 = \)
\( 25x^4 y^4 : (25x^2 y^4) -3x^2 = \)
\( x^{4-2} y^{4-4} – 3x^2 = x^2 – 3x^2 = -2x^2 \)
- Es. 4:
\( \big[(-x^3y)^2 \big(-\frac{1}{4}xy^2\big) + \frac{3}{2}x^3y^2\big(-\frac{1}{3}x^2y\big)^2\big] : \big[\frac{1}{4}xy(-x^3y)^2\big] = \)
\( \big[(x^6y^2) \big(-\frac{1}{4}xy^2\big)+\big(\frac{3}{2}x^3y^2\big)\big(\frac{1}{9}x^4y^2\big)\big] : \big[\frac{1}{4}xy(x^6y^2)\big] = \)
\( \big[-\frac{1}{4}x^{6+1}y^{2+2}+\frac{3}{2}\times \frac{1}{9}x^{3+4}y^{2+2}\big] : \big[\frac{1}{4}x^{1+6}y^{1+2}\big] = \)
\( \big[-\frac{1}{4}x^7y^4 + \frac{1}{6}x^7 y^4\big] : \big[\frac{1}{4}x^7y^3\big] = \)
\( \big[\big(-\frac{1}{4} + \frac{1}{6}\big)x^7y^4\big] : \big[\frac{1}{4}x^7y^3\big] = \)
\( \big[-\frac{1}{12}x^7y^4\big] : \big[\frac{1}{4}x^7y^3\big] = \)
\( -\frac{1}{12} \times 4 x^{7-7} y^{4-3} = -\frac{1}{3} y \)
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Videolezione sulla riduzione di un monomio in forma normale