Factorise the expression: frac{x^{2}}{4}+frac | vedclass

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Question

(A) The given expression is $\frac{x^{2}}{4}+\frac{3 x y}{5}+\frac{9 y^{2}}{25}$.This can be written in the form $a^{2} + 2ab + b^{2} = (a + b)^{2}$.H

Vedclass · Accepted Answer

$\left(\frac{x}{2}+\frac{3 y}{5}\right)^{2}$

Vedclass · Answer

(A) The given expression is $\frac{x^{2}}{4}+\frac{3 x y}{5}+\frac{9 y^{2}}{25}$.This can be written in the form $a^{2} + 2ab + b^{2} = (a + b)^{2}$.Here,$a^{2} = \frac{x^{2}}{4} \implies a = \frac{x}{2}$.And $b^{2} = \frac{9 y^{2}}{25} \implies b = \frac{3 y}{5}$.Now,check the middle term $2ab = 2 	imes \left(\frac{x}{2}ight) 	imes \left(\frac{3 y}{5}ight) = \frac{3 x y}{5}$.Since the middle term matches,the expression is $\left(\frac{x}{2}+\frac{3 y}{5}ight)^{2}$.

Factorise the expression: $\frac{x^{2}}{4}+\frac{3 x y}{5}+\frac{9 y^{2}}{25}$

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