Question

Розкладіть на множники:
1)
${a}^{2} + 6a - {b}^{2} + 4b + 5$
2)
$3 {x}^{2} - 4xy + {y}^{2} + 4x - 4$
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Answer 1

1) a² + 6a - b² + 4b + 5 = a² + 6a - b² + 4b + 9 - 4 = (a² + 6a + 9) - (b² - 4b + 4) = (a + 3)² - (b - 2)² = ( a + 3 - b + 2)(a + 3 + b - 2) = (a - b + 5)(a + b + 1)

2) 3x² - 4xy + y² + 4x - 4 = 4x² - x² - 4xy + y² + 4x - 4 = (4x² - 4xy + y²) -

= (x² - 4x + 4) = (2x - y)² - (x - 2)² = (2x - y - x + 2)(2x - y + x - 2) =

= (x - y + 2)(3x - y - 2)