Transcripción 15/3/2026, 11:13:21 a.m.

Apuntes

• Algebraic Expressions and Simplifications: 10/03/2026 a) Simplification of the expression \( 4X^3 \cdot y^3 \div 2X \cdot y^4 \) The calculation proceeds as follows: \[ \frac{4X^3 \cdot y^3}{2X \cdot y^4} \equiv \frac{4}{2} \cdot \frac{X^3}{X} \cdot \frac{y^3}{y^4} = 2 \cdot X^{3-1} \cdot y^{3-4} = 2 \cdot X^2 \cdot y^{-1} \] Expressed with negative exponents: \[ 2 \cdot X^2 \cdot y^{-1} = 2 \cdot X^2 \cdot \frac{1}{y} = \frac{2X^2}{y} \] Note: The original transcription had an inconsistency; the simplified form should be \( 2X^2 y^{-1} \), not \( 2X^{-2} y^4 \). b) Logarithmic expressions: \[ | \log A = 2 \log X + \log Y + 4 \log Z - \log \varepsilon \] Rearranged as: \[ \log A = (\log X^2 + \log Y) + (\log Z^4 - \log \varepsilon) \] And the expression: \[ \log \varepsilon = \log \left( \frac{X^3 \cdot Y \cdot Z^4}{\varepsilon} \right) \] --- • Polynomial and Algebraic Operations: 11/03/2026 The sequence of polynomial operations appears to be a series of simplifications or combining like terms: Starting with: \[ a - a^5 - 3a^2 \] Adding the polynomial: \[ a^2 + 2a + 1 \] Results in: \[ (-a^2 + 2a^2 - 3a + 1) \Rightarrow \text{which simplifies to} \quad -a^2 ...