Simplify: $(3 x - 2 y) (3 x + 4 y) - (3 x + 2 y) (3 x - 2 y)$ $[3 M a r k s]$

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Solution

$(3 x - 2 y) (3 x + 4 y) - (3 x + 2 y) (3 x - 2 y)$ $[0.5 M a r k]$

Using identity $(a + b) (a - b) = a^{2} - b^{2}$ ,
$(3 x + 2 y) (3 x - 2 y) = 9 x^{2} - 4 y^{2}$ $[1 M a r k]$

So, $(3 x - 2 y) (3 x + 4 y) - (3 x + 2 y) (3 x - 2 y)$
= $(9 x^{2} + 6 x y - 8 y^{2}) - [9 x^{2} - 4 y^{2}]$
= $- 4 y^{2} + 6 x y$ $[1.5 M a r k s]$

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Factorise :

$4 x (3 x - 2 y) - 2 y (3 x - 2 y)$

Find the continued products:
(i) $(x + 1) (x - 1) (x^{2} + 1)$
(ii) $(x - 3) (x + 3) (x^{2} + 9)$
(iii) $(3 x - 2 y) (3 x + 2 y) (9 x^{2} + 4 y^{2})$
(iv) $(2 p + 3) (2 p - 3) (4 p^{2} + 9)$

Simplify: (3x-2y)(3x+4y)-(3x+2y)(3x-2y)

Q. Simplify:

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

Q. Simplify : (3x + 2y)(3x + 4y) =

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Simplify: (3x−2y)(3x+4y)−(3x+2y)(3x−2y) [3 Marks]

(3x−2y)(3x+4y)−(3x+2y)(3x−2y) [0.5 Mark] Using identity (a+b)(a−b)=a2−b2, (3x+2y)(3x−2y)=9x2−4y2 [1 Mark] So, (3x−2y)(3x+4y)−(3x+2y)(3x−2y) =(9x2+6xy−8y2)−[9x2−4y2] = −4y2+6xy [1.5 Marks]

Simplify: $(3 x - 2 y) (3 x + 4 y) - (3 x + 2 y) (3 x - 2 y)$ $[3 M a r k s]$