Question

Descompuneti în factori:
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Answer 1

Răspuns:

$a) {a}^{2} + 2ab + {b}^{2} + 5a + 5b = ( {a + b)}^{2} + 5(a + b) = \\ = (a + b)(a + b + 5) \\ b) {x}^{2} - 2x + 1 + a(x - 1) = ( {x - 1)}^{2} + a(x - 1) = \\ = (x - 1)(x - 1 + a)$

$f)( {2a - b})^{2} - 4 {a}^{2} + {b}^{2} = \\ =4 {a}^{2} - 4ab + {b}^{2} - 4 {a}^{2} + {b}^{2} = \\ = - 4ab + 2 {b}^{2} = 2b( - 2a + b)$

$g) {x}^{2} + 8x + 16 - {b}^{2} = \\ = ( {x + 4)}^{2} - {b}^{2}$

$h)( {3x - {a}^{3} })^{2} - 18 {x}^{2} + 2 {a}^{6} = \\ = 9 {x}^{2} - 2 \times 3x \times {a}^{3} + {a}^{6} - 18 {x}^{2} + 2 {a}^{6} = \\ = - 9 {x}^{2} - 6x {a}^{3} + 3 {a}^{6} = \\ = - 3x (3x + 2 {a}^{3} ) + 3 {a}^{6}$

$j)( {x}^{2} - 6x + 9) - {a}^{2} = ( {x - 3})^{2} - {a}^{2}$

$k)2 {a}^{2} - 2 {b}^{2} = 2( {a}^{2} - {b}^{2} ) = 2 \times (a - b)(a + b)$

$l)3 {x}^{2} - 12 = 3( {x}^{2} - 4) = \\ = 3( {x}^{2} - 2)( {x}^{2} + 2)$

$m)4 {x}^{2} - {a}^{2} + 14x + 7a = \\ 2x(2x + 7) - a(a - 7)$

$n)3 {a}^{2} - 16 = 3( {a}^{2} - 4)( {a}^{2} + 4) = 3(a - 2)(a + 2)$

$c)4 {a}^{2} + 4a + 1 + 2ax + x = ( {2a + 1)}^{2} + x(2a + 1) = (2a + 1)(2a + 1 + x)$

$d)3 {x}^{2} - 2x \sqrt{3} + 1 + 3x \sqrt{3} - 3 = ( \sqrt{3} x - 1) ^{2} + 3( \sqrt{3} x - 1) = ( \sqrt{3} x - 1)( \sqrt{3} x - 1 + 3) = ( \sqrt{3} x - 1)( \sqrt{3} x + 2)$

$e)(x + y) ^{2} + {x}^{2} - {y}^{2} = \\ = ( {x + y})^{2} + (x + y)(x - y) = (x + y)(x + y + x - y) = (x + y) \times 2x$