Question

10. Fatore os trinômios quadrados perfeitos. a) x² + 2x + 1= b) x² + 10x + 25= c) 9x² + 6x + 1= d) 36a^4 + 12a²b³ + b^6= e) a² - 2a + 1= f) y² - 8xy + 16x² g) 49 - 14a + a² h) 1 - 2abc + a²b²c² i) a²b² - 2abx + x² j) a² - 2/3a + 1/9

Answer 1

Resposta:

$a) {x}^{2} + 2x + 1 = (x + 1) ^{2} \\ b) {x}^{2} + 10x + 25=(x + 5) ^{2} \\ c) {9x}^{2} + 6x + 1=(3x + 1) ^{2} \\ d)36 {a}^{4} + 12 {a}^{2} {b}^{3} + b^6= ({b}^{2} + 6 {a}^{2} )^{2} \\ e) {a}^{2} - 2a + 1=(a - 1)^{2} \\ f) {y}^{2} - 8xy + 16 {x}^{2} = {y}^{2} - 8xy + 16 {x}^{2} \\ g)49 - 14a + {a}^{2} = (a - 7) ^{2} \\ h)1 - 2abc + {a}^{2} {b}^{2} {c}^{2} = {a}^{2} {b}^{2} {c}^{2} - 2abc + 1 \\ i) {a}^{2} {b}^{2} - 2abx + {x}^{2} = {x}^{2} + {a}^{2} {b}^{2} - 2abx \\ j) {a}^{2} - \frac{2}{3 {}^{a} } + \frac{1}{9} = \frac{(3a - 1) ^{2} }{9}$