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# 4.Divide as directed. (i) $$5(2x + 1)(3x + 5) ÷ (2x + l)$$ (ii) $$26xy (x + 5) (y – 4) ÷ 13x (y – 4)$$ (iii) $$52pqr (p + q) (q + r) (r + p) ÷104pq (q + r) (r + p)$$ (iv) $$20 (y + 4) (y^2 + 5y + 3) ÷ 5 (y + 4)$$ (v) $$x (x + 1) (x + 2) (x + 3) ÷ x (x + 1)$$

(i)Given: $$5(2x + 1)(3x + 5) ÷ (2x + 1)$$

$$=\frac{5(2x + 1)(3x + 5)}{2x + 1}=\frac{5\times (2x+3)\times(3x + 5)}{(2x + 1)}$$

$$=\frac{5\times (3x+5)}1=5(3x+5)$$

(ii)Given: $$26xy (x + 5) (y – 4) ÷ 13x (y – 4)$$

$$=\frac{26xy (x + 5) (y – 4)}{13x (y – 4)}=\frac{13\times 2\times x \times y \times (x+5) \times (y-4)}{13\times x\times (y-4)}$$

$$=\frac{2\times y \times (x+5))}1=2y(x+5)$$

(iii)Given: $$52pqr (p + q) (q + r) (r + p) ÷104pq (q + r) (r + p)$$

$$=\frac{52pqr (p + q) (q + r) (r + p)}{104pq (q + r) (r + p)}=\frac{52\times p \times q \times r \times (p+q) \times (q+r) \times (r+p)}{52\times 2 \times p \times q \times (q+r) \times (r+p)}$$

$$=\frac{1}2r(p+q)$$

(iv)Given: $$20 (y + 4) (y^2 + 5y + 3) ÷ 5 (y + 4)$$

$$=\frac{20 (y + 4) (y^2 + 5y + 3) }{5 (y + 4)}=\frac{5\times 4 \times (y+4) \times (y^2+5y+3)}{13\times x\times (y-4)}$$

$$=\frac{4\times (y^2 + 5y + 3)}1=4(y^2 + 5y + 3)$$

(v)Given: $$x (x + 1) (x + 2) (x + 3) ÷ x (x + 1)$$

$$=\frac{x (x + 1) (x + 2) (x + 3) }{x (x + 1)}=\frac{z \times (x+1) \times (x+2) \times (x+3)}{x \times (x+1)}$$

$$=\frac{(x+2)(x+3)}1=(x+2)(x+3)$$