Divide12 x y 9 x 2 - 16 y 2 - 4 x y 3 x - 4 y

9 x^2 16 y^2=(3 x)^2 (4 y)^2=(3 x 4 y)(3 x+4 y) (12xy(9 x^2 16 y^2))÷ (4xy(3 x+4 y))=12 x y(9 x^2 16 y^2)4 x y(3 x+4 y)=12 x y(3 x 4 y)(3 x+4 y)4 x y( ...

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Byju's Answer

Standard IX

Mathematics

Long Division Method to Divide Two Polynomials

Divide12 x y...

Question

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

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Solution

$9 x^{2} - 16 y^{2} = (3 x)^{2} - (4 y)^{2} = (3 x - 4 y) (3 x + 4 y)$

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

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Divide12xy(9x2−16y2)÷4xy(3x+4y)

9x2−16y2=(3x)2−(4y)2=(3x−4y)(3x+4y)(12xy(9x2−16y2))÷(4xy(3x+4y))=12xy(9x2−16y2)4xy(3x+4y)=12xy(3x−4y)(3x+4y)4xy(3x+4y)=3(3x−4y)

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

$9 x^{2} - 16 y^{2} = (3 x)^{2} - (4 y)^{2} = (3 x - 4 y) (3 x + 4 y)$

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