Simplify- 3x-2y3x-4y-3x-2y3x-2y-4y2-6xy

To simplify: nbsp; (3x 2y)(3x+4y) (3x+2y)(3x 2y)/( 4y^2+6xy) Using identity (a+b) (a b) = a^2 b^2, nbsp; (3x+2y)(3x 2y)= 9x^2 4y^2 So, the numerator can ...

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Byju's Answer

Standard VIII

Mathematics

Multiplication of Polynomials

Simplify: 3x-...

Question

Simplify: $\frac{(3 x - 2 y) (3 x + 4 y) - (3 x + 2 y) (3 x - 2 y)}{(- 4 y^{2} + 6 x y)}$

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Solution

To simplify: $\frac{(3 x - 2 y) (3 x + 4 y) - (3 x + 2 y) (3 x - 2 y)}{(- 4 y^{2} + 6 x y)}$

Using identity $(a + b) (a - b) = a^{2} - b^{2}$ ,
$(3 x + 2 y) (3 x - 2 y) = 9 x^{2} - 4 y^{2}$

So, the numerator can be simplified as
$(3 x - 2 y) (3 x + 4 y) - (3 x + 2 y) (3 x - 2 y)$
$= (9 x^{2} + 6 x y - 8 y^{2}) - [9 x^{2} - 4 y^{2}]$
$= - 4 y^{2} + 6 x y$

Then,
$\frac{(3 x - 2 y) (3 x + 4 y) - (3 x + 2 y) (3 x - 2 y)}{(- 4 y^{2} + 6 x y)} \Rightarrow \frac{- 4 y^{2} + 6 x y}{- 4 y^{2} + 6 x y} = 1$

Suggest Corrections

Simplify: (3x−2y)(3x+4y)−(3x+2y)(3x−2y)(−4y2+6xy)

Simplify: $\frac{(3 x - 2 y) (3 x + 4 y) - (3 x + 2 y) (3 x - 2 y)}{(- 4 y^{2} + 6 x y)}$