question_answer 1)

                Factorize:                 (i) \[{{x}^{2}}+xy+8x+8y\]                                                            (ii) \[15xy-6x+5y-2\]                 (iii) \[ax+bx-ay-by\]                                                        (iv) \[15pq+15+9q+25p\]                 (v) \[z-7+7xy-xyz\].

Answer:

                (i) \[{{x}^{2}}+xy+8x+8y\]                 \[{{x}^{2}}+xy+8x+8y\] \[=x(x+y)+8(x+y)\] \[=(x+y)(x+8)\]                                 |Taking \[(x+y)\]common (ii) \[15xy-6x+5y-2\] \[15xy-6x+5y-2\] \[=3x(5y-2)\,+(5y-2)\]                   |Taking \[(5y-2)\] common                 (iii) \[ax+bx-ay-by\]        \[ax+bx-ay-by\] \[=x(a+b)\,-y(a+b)\] \[=(a+b)\,(x-y)\]                                              |Taking \[(a+b)\]common                 (iv) \[15pq+15+9q+25p\]                 \[15pq+15+9q+25p\] \[=15pq+9q+25p+15\] \[=3q(5p+3)\,+5(5p+3)\] \[=(5p+3)\,(3q+5)\]                        |Taking \[(5p+3)\]common                 (v) \[z-7+7xy-xyz\]          \[z-7+7xy-xyz\] \[=z-7-xyz+7xy\] \[=1(z-7)\,-xy\,(z-7)\]    \[=(z-7)\,(1-xy)\]                             |Taking \[(z-7)\]common