Factorise the expressions and divide them as directed. $12 x y (9 x^{2} - 16 y^{2}) + 4 x y (3 x + 4 y)$

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Solution

Factorise the numerator
$12 x y (9 x^{2} - 16 y^{2}) \div 4 x y (3 x + 4 y) = 12 x y {(3 x)^{2} - (4 y z)^{3}}$
$= 12 x y (3 x - 4 y) (3 x + 4 y)$

Cancel out the common factors from numerator and denminator
$12 x y (3 x - 4 y) (3 x + 4 y) 3 (3 x - 4 y)$
$4 x y (3 x + 4 y) 1$
$= 3 (3 x - 4 y)$

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Similar questions

12 x y (9 x^{2} - 16 y^{2}) \div 4 x y (3 x + 4 y)

12 x y (9 x^{2} - 16 y^{2}) \div 4 x y (3 x + 4 y)

12 x y (9 x^{2} - 16 y^{2}) \div 4 x y (3 x + 4 y)

12 x y (9 x^{2} - 16 y^{2})

\div

4 x y (3 x + 4 y)

Factorise the expressions and divide them as directed.

(i) (y² + 7y + 10) ÷ (y + 5)

(ii) (m² − 14m − 32) ÷ (m + 2)

(iii) (5p² − 25p + 20) ÷ (p − 1)

(iv) 4yz(z² + 6z − 16) ÷ 2y(z + 8)

(v) 5pq(p² − q²) ÷ 2p(p + q)

(vi) 12xy(9x² − 16y²) ÷ 4xy(3x + 4y)

(vii) 39y³(50y²− 98) ÷ 26y²(5y+ 7)

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