Question

Factorize: (x+y)^2 + 5(x+y) - 36

Answer 1

Step-by-step explanation:

$\qquad\qquad\sf {:}\leadsto (x+y)^2+5 (x+y)-36$

$\qquad\qquad\sf {:}\leadsto x^2+2xy+y^2+5x+5y-36$

$\qquad\qquad\sf {:}\leadsto x^2+y^2+2xy+5x+5y-36$

$\qquad\qquad\sf {:}\leadsto x^2+5x+2xy+y^2+5y-36$

$\qquad\qquad\sf {:}\leadsto x (x+5)+y (y+5)+2(xy-18)$

$\qquad\qquad\sf {:}\leadsto (y+5)(x+5)(xy-18)(x+y+2)$

$\qquad\qquad\sf {:}\leadsto (5+x)(5+y)(xy-18)(x+y+2)$

$\qquad\qquad\sf {:}\leadsto 5^2+(x+y)5+xy(xy-18)(x+y+2)$

$\qquad\qquad\sf {:}\leadsto 25+5 (x+y)+xy (x+y+2)(xy-18)$

$\qquad\qquad\sf {:}\leadsto 25+(x+y)(1+2)+xy (1-18)$

$\qquad\qquad\sf {:}\leadsto 25+3 (x+y)-17xy$