Simplify the following.
(a) $ (2 a+3)^{2}-(2 a-3)^{2} $
(b) $ (3.5 x-1.5 y)^{2}-(1.5 x-3.5 y)^{2} $

To do:

We have to find the value of the below expressions using suitable properties.

(a) \( (2 a+3)^{2}-(2 a-3)^{2} \)
(b) \( (3.5 x-1.5 y)^{2}-(1.5 x-3.5 y)^{2} \)

Solution:

We know that,

$(a+b)^2=a^2+2ab+b^2$

$(a-b)^2=a^2-2ab+b^2$

Therefore,

(a) $(2 a+3)^{2}-(2 a-3)^{2}=(2a)^2+2\times2a \times3+(3)^2-[(2a)^2-2\times2a\times3+(3)^2]$

$=4a^2+12a+9-[4a^2-12a+9]$

$=4a^2-4a^2+12a+12a+9-9$

$=24a$

(b) $(3.5 x-1.5 y)^{2}-(1.5 x-3.5 y)^{2}=(3.5x)^2-2\times3.5x \times1.5y+(1.5y)^2-[(1.5x)^2-2\times1.5x\times3.5y+(3.5y)^2]$

$=12.25x^2+10.5xy+2.25y^2-[2.25x^2-10.5xy+12.25y^2]$

$=12.25x^2-2.25x^2+10.5xy+10.5xy+2.25y^2-12.25y^2$

$=10x^2+21xy-10y^2$

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Updated on: 10-Oct-2022

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