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# 3.Factorise: (i) $$x2 + xy + 8x + 8y$$ (ii) $$15xy – 6x + 5y – 2$$ (iii) $$ax + bx – ay – by$$ (iv) $$15pq + 15 + 9q + 25p$$ (v) $$z – 7 + 7xy – xyz$$

(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 =$$-(1 – xy) (z – 7)$$