1. $$ (x+3)(x-3)= $$ 2. $$ (3 x+5 y)(3 x-5 y)= $$ 3. $$ \left(6 x^{5}+1\right)\left(6 x^{5}-1\right)= $$ 4. $$ \left(9 a b^{4}-c^{7}\right)\left(9 a b^{4}+c^{7}\right)= $$ 5. $$ \left(\frac{3}{5} m+\frac{1}{2}\right)\left(\frac{3}{5} m-\frac{1}{2}\right)= $$ 6. $$ \left(\frac{7}{6} x^{3}+\frac{3}{2}\right)\left(\frac{7}{6} x^{3}-\frac{3}{2}\right)= $$ 7. $$ \left(\frac{1}{3} x y+z^{6}\right)\left(\frac{1}{3} x y-z^{6}\right)= $$ 8. $$ \left(3 x^{2}+\frac{1}{10}\right)\left(-3 x^{2}+\frac{1}{10}\right)= $$

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UpStudy AI · Accepted Answer

Claro, a continuación se expanden las expresiones dadas:

1. $$ (x + 3)(x - 3) = x^{2} - 9 $$

2. $$ (3x + 5y)(3x - 5y) = 9x^{2} - 25y^{2} $$

3. $$ (6x^{5} + 1)(6x^{5} - 1) = 36x^{10} - 1 $$

4. $$ (9ab^{4} - c^{7})(9ab^{4} + c^{7}) = 81a^{2}b^{8} - c^{14} $$

5. $$ \left(\frac{3}{5}m + \frac{1}{2}\right)\left(\frac{3}{5}m - \frac{1}{2}\right) = \frac{9}{25}m^{2} - \frac{1}{4} $$

6. $$ \left(\frac{7}{6}x^{3} + \frac{3}{2}\right)\left(\frac{7}{6}x^{3} - \frac{3}{2}\right) = \frac{49}{36}x^{6} - \frac{9}{4} $$

7. $$ \left(\frac{1}{3}xy + z^{6}\right)\left(\frac{1}{3}xy - z^{6}\right) = \frac{1}{9}x^{2}y^{2} - z^{12} $$

8. $$ \left(3x^{2} + \frac{1}{10}\right)\left(-3x^{2} + \frac{1}{10}\right) = -9x^{4} + \frac{1}{100} $$

Estas expansiones se han realizado utilizando la identidad de la diferencia de cuadrados, que establece que $$(a + b)(a - b) = a^{2} - b^{2}$$.
1. $$ (x + 3)(x - 3) = x^{2} - 9 $$ 2. $$ (3x + 5y)(3x - 5y) = 9x^{2} - 25y^{2} $$ 3. $$ (6x^{5} + 1)(6x^{5} - 1) = 36x^{10} - 1 $$ 4. $$ (9ab^{4} - c^{7})(9ab^{4} + c^{7}) = 81a^{2}b^{8} - c^{14} $$ 5. $$ \left(\frac{3}{5}m + \frac{1}{2}\right)\left(\frac{3}{5}m - \frac{1}{2}\right) = \frac{9}{25}m^{2} - \frac{1}{4} $$ 6. $$ \left(\frac{7}{6}x^{3} + \frac{3}{2}\right)\left(\frac{7}{6}x^{3} - \frac{3}{2}\right) = \frac{49}{36}x^{6} - \frac{9}{4} $$ 7. $$ \left(\frac{1}{3}xy + z^{6}\right)\left(\frac{1}{3}xy - z^{6}\right) = \frac{1}{9}x^{2}y^{2} - z^{12} $$ 8. $$ \left(3x^{2} + \frac{1}{10}\right)\left(-3x^{2} + \frac{1}{10}\right) = -9x^{4} + \frac{1}{100} $$

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