Find the value of the following using suitable properties
(a) $ (3 x+4 y)^{2} $
(b) $ (0.2 x-0.3 y)^{2} $
(c) $ (x+3)(x-5) $
(d) $ \left(x-y^{2}\right)^{2} $

To do:

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

(a) \( (3 x+4 y)^{2} \)
(b) \( (0.2 x-0.3 y)^{2} \)
(c) \( (x+3)(x-5) \)
(d) \( \left(x-y^{2}\right)^{2} \)

Solution:

We know that,

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

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

$(a+b)(c+d)=ac+ad+bc+bd$

Therefore,

(a) $(3x+4y)^2=(3x)^2+2\times3x \times4y+(4y)^2$

$=9x^2+24xy+16y^2$

(b) $(0.2 x-0.3 y)^{2}=(0.2x)^2-2\times0.2x\times0.3y+(0.3y)^2$

$=0.04x^2-0.06xy+0.09y^2$

(c) $(x+3)(x-5)=x \times x+x \times (-5)+3\times x+3\times(-5)$

$=x^2-5x+3x-15$

 $=x^2-2x-15$

(d) $ (x-y^{2})^{2}=(x)^2-2\times x \times y^2+(y^2)^2$

$=x^2-2xy^2+y^4$