Factorise the expression and divide them as directed: (i)(y² + 7y + 10) ÷ (y + 5) (ii)(m² - 6m - 8) ÷ (m + 2) (iii)(5p² - 5p + 20) ÷ (p - 5) (iv)4yz(z² + 6z - 8) ÷ 2y(z + 8) (v)(5pq(p² - q²)) ÷ 2p(p + q) (vi)12xy(9x² - 8y²) ÷ 4xy(3x + 4y) (vii)39y³(50y² - 7) ÷ 26y²(5y + 7)

(i)(y² + 7y + 10) ÷ (y + 5) = (y² + 5y + 2y + 10) ÷ (y + 5) = y(y + 5) + 2(y + 5) ÷ (y + 5) = (y + 5)(y + 2) ÷ (y + 5) = y + 2
(ii)(m² - 6m - 8) ÷ (m + 2) = (m² - 8m + 2m - 8) ÷ (m + 2) = m(m - 8) + 2(m - 8) ÷ (m + 2) = (m - 8)(m + 2) ÷ (m + 2) = m - 8
(iii)(5p² - 5p + 20) ÷ (p - 5) = (5p² - 25p + 20p + 20) ÷ (p - 5) = 5p(p - 5) + 20(p - 5) ÷ (p - 5) = (p - 5)(5p + 20) ÷ (p - 5) = 5p + 20 = 5(p + 4)
(iv)4yz(z² + 6z - 8) ÷ 2y(z + 8) = (4yz)(z² + 8z - 2z - 8) ÷ 2y(z + 8) = (2z)z(z + 8) - 2(z + 8)(z + 8) = (2z)(z - 2)(z + 8) ÷ (z + 8) = 2z(z - 2)
(v)5pq(p² - q²) ÷ 2p(p + q) = (5pq)(p - q)(p + q) ÷ 2p(p + q) = 5q(p - q) ÷ 2 = (5q(p - q))/2
(vi)12xy(9x² - 8y²) ÷ 4xy(3x + 4y) = (12xy)[(3x)² - (4y)²] ÷ 4xy(3x + 4y) = (12xy)(3x - 4y)(3x + 4y) ÷ 4xy(3x + 4y) = 3(3x - 4y)
(vii)39y³(50y² - 7) ÷ 26y²(5y + 7) = 39y³ × 2 × (25y² - 7) ÷ 26y²(5y + 7) = (3y)[(5y)² - 7] ÷ (5y + 7) = (3y)[(5y - √7)(5y + √7)] ÷ (5y + 7) = 3y(5y - √7)(5y + √7)/(5y + 7)