Question

Va rog frumos exercitiul 5 !

Answer 1

a)25(a+b-c)
b)(x-1)[(2x+3)(3x+2)]
c)(a+1)[(x-2)+5x]
d)(a+2)(2y-3x)
e)√7x(3-5y)

Answer 2

$a)25a + 25b - 25c = 25(a + b - c)$

$b)(x - 1)(2x + 3) + (x - 1)(3x + 2) = (x - 1)(2x + 3 + 3x + 2) = (x - 1)(5x +5) = (x - 1) \times 5(x + 1)$

$c)(x - 2)(a + 1) + 5x(a + 1) = (a + 1)(x - 2 + 5x) = (a + 1)(6x - 2) = (a + 1) \times 2(3x - 1)$

$d) - 3x(a + 2) + 2y(a + 2) = (a + 2)( - 3x + 2y)$

$e)3 \sqrt{7} x - 5 \sqrt{7} yx = \sqrt{7} x( 3 - 5y)$

$f)8a + 16 {a}^{2} + 24 {a}^{3} = 8a(1 + 2a + 3 {a}^{2} )$

$g)3 {x}^{6} + 9 {x}^{5} - 12 {x}^{4} + 33 {x}^{3} = 3 {x}^{3} ( {x}^{3} + 3 {x}^{2} - 4x + 11)$

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

$i)30 {x}^{5} {y}^{4} {z}^{4} + 60 {x}^{3} {y}^{6} {z}^{3} - 180 {x}^{6} {y}^{3} {z}^{5} = 30 {x}^{3} {y}^{3} {z}^{3} ( {x}^{2} yz + 2 {y}^{3} - 6 {x}^{3} {z}^{2} )$

$j)24 {a}^{3} {b}^{3} {c}^{4} - 48 {a}^{2} {b}^{2} {c}^{3} - 72 {a}^{2} {b}^{2} {c}^{2} = 24 {a}^{2} {b}^{2}{c}^{2}(ab {c}^{2} - 2c - 3)$