Factorise the expression: frac{4x^2}{9} - fra | vedclass

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Question

(A) The given expression is $\frac{4x^2}{9} - \frac{x}{3} + \frac{1}{16}$.This can be rewritten in the form $a^2 - 2ab + b^2 = (a - b)^2$.Here,$a^2 =

Vedclass · Accepted Answer

$\left(\frac{2x}{3} - \frac{1}{4}\right)^2$

Vedclass · Answer

(A) The given expression is $\frac{4x^2}{9} - \frac{x}{3} + \frac{1}{16}$.This can be rewritten in the form $a^2 - 2ab + b^2 = (a - b)^2$.Here,$a^2 = \frac{4x^2}{9} \implies a = \frac{2x}{3}$.And $b^2 = \frac{1}{16} \implies b = \frac{1}{4}$.Checking the middle term: $-2ab = -2 	imes \left(\frac{2x}{3}ight) 	imes \left(\frac{1}{4}ight) = -\frac{4x}{12} = -\frac{x}{3}$.Since the middle term matches,the expression is $\left(\frac{2x}{3} - \frac{1}{4}ight)^2$.

Factorise the expression: $\frac{4x^2}{9} - \frac{x}{3} + \frac{1}{16}$

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