Question

can any one factories the question of each

Answer 1

1.

ab( x^2 + 1) + x (a^2 + b^2)

= abx^2 + ab + a^2x + b^2x
=abx^2 + a^2 x + b^2 x + ab

= ax(bx + a) + b( bx +a)
= (ax+b)(bx + a)


2.
x^2 - (a+b)x + ab
= x^2 - ax - bx + ab
= x(x -a) -b( x-a)
= (x-b)(x-a)

3.

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



4.
${x}^{2} - 24 x- 180 \\ {x}^{2} - 30x + 6x - 180 \\ x(x - 30) + 6(x - 30) \\ (x - 30) + (x + 6)$
5.
$5 \sqrt{5} {x}^{2} + 20x + 3 \sqrt{5} \\ 5 \sqrt{5} {x}^{2} + 15x + 5x + 3 \sqrt{5} \\ \sqrt{5} x(5x + 3\sqrt{5} ) + (5x + 3 \sqrt{5}) \\ ( \sqrt{5} x + 1)(5x + 3 \sqrt{5} )$