Question

(3x - 3)² - (2x - 7) = (3x - 5)(3x + 5)

Answer 1

Explicación paso a paso:

$(3x - 3) ^{2} - (2x - 7) = (3x - 5)(3x + 5) \\ 9 {x}^{2} - 18x+ 9 - 2x + 7 = 9 {x}^{2} - 25 \\ 9 {x}^{2} - 20x + 16 = 9 {x}^{2} - 25 \\ 9 {x}^{2} - 9 {x}^{2} - 20x = - 25 - 16 \\ - 20x = - 41 \\ x = \frac{41}{20} \\ \\ comprobamos \\ (3 \times \frac{41}{20} - 3)^{2} - (2 \times \frac{41}{20} - 7) = (3 \times \frac{41}{20} - 5)(3 \times \frac{41}{20} + 5) \\ \\ ( { \frac{123}{20} - 3})^{2} - ( \frac{82}{20} - 7) = ( \frac{123}{20} - 5)( \frac{123}{20} + 5) \\ \\ (\frac{123 - 60}{20} )^{2} - ( \frac{82 - 140}{20} ) = ( \frac{123 - 100}{20} )( \frac{123 + 100}{20} ) \\ \\ ( { \frac{63}{20} )}^{2} - ( - \frac{58}{20} ) = \frac{23}{20} \times \frac{223}{20} \\ \\ \frac{3969}{400} + \frac{58}{20} = \frac{5129}{400} \\ \\ \frac{3969 + 1160}{400} = \frac{5129}{400} \\ \\ \frac{5129}{400} = \frac{5129}{400}$