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Answer :
(i)We have: \(x2 + xy + 8x + 8y\)
now, grouping the terms, we have
\(x2 + xy + 8x + 8y\)
\(= x(x + y) + 8(x + y)\)
\(= (x + y)(x + 8)\)
Thus, the required factors =\((x + y)(x + 8)\)
(ii)We have: \(15xy – 6x + 5y – 2\)
Now, grouping the terms, we have
\((15xy – 6x) + (5y – 2)\)
\(= 3x(5y – 2) + (5y – 2)\)
\(= (5y – 2)(3x + 1)\)
Thus, the required factors =\( (5y – 2)(3x + 1)\)
(iii) We have: \(ax + bx – ay – by\)
Now, grouping the terms, we have
\(= (ax – ay) + (bx – by)\)
\(= a(x – y) + b(x – y)\)
\(= (x – y)(a + b)\)
Thus, the required factors = \((x – y)(a + b)\)
(iv) We have: \(15pq + 15 + 9q + 25p\)
Now, grouping the terms, we have
\(= (15pq + 25p) + (9q + 15)\)
\(= 5p(3q + 5) + 3(3q + 5)\)
\(= (3q + 5) (5p + 3)\)
Thus, the required factors = \((3q + 5) (5p + 3)\)
(v) We have:\(z – 7 + 7xy – xyz\)
Now,grouping the terms, we have
\(= (-xyz + 7xy) + (z – 7)\)
\(= -xy(z – 7) + 1 (z – 7)\)
\(= (-xy + 1) (z – 1)\)
Thus, the required factor =\( -(1 – xy) (z – 7)\)