Question

Using identities factorize it. (x-2)square +9(x-2) by (x+7)​

Answer 1

Step-by-step explanation:

$\frac{( {x - 2)}^{2} + 9(x - 2) }{(x + 7)}$

$= \frac{( {x}^{2} - 2 \times x \times 2 + ( {2)}^{2} + 9(x - 2)}{x + 7}$

$= \frac{ ({x}^{2} - 4x + 4) + 9x - 18 }{x + 7}$

$= \frac{ {x}^{2} - 4x + 4 + 9x - 18}{x + 7}$

$= \frac{ {x}^{2} + 5x - 14 }{x + 7}$

$= \frac{ {x}^{2} + (7 - 2)x - 14}{x + 7}$

$= \frac{ {x}^{2} + 7x - 2x - 14}{x + 7}$

$= \frac{ x(x + 7) - 2(x + 7) }{x + 7}$

$= \frac{(x + 7)(x - 2)}{x + 7}$

$= (x - 2)$