Expand left(frac{2x}{3} + frac{3y}{4}right)^{ | vedclass

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Question

(A) To expand the expression $\left(\frac{2x}{3} + \frac{3y}{4}\right)^{2}$,we use the algebraic identity $(a + b)^{2} = a^{2} + 2ab + b^{2}$.Here,$a

Vedclass · Accepted Answer

$\frac{4}{9}x^{2} + xy + \frac{9}{16}y^{2}$

Vedclass · Answer

(A) To expand the expression $\left(\frac{2x}{3} + \frac{3y}{4}\right)^{2}$,we use the algebraic identity $(a + b)^{2} = a^{2} + 2ab + b^{2}$.Here,$a = \frac{2x}{3}$ and $b = \frac{3y}{4}$.Substituting these values into the identity:$\left(\frac{2x}{3} + \frac{3y}{4}\right)^{2} = \left(\frac{2x}{3}\right)^{2} + 2\left(\frac{2x}{3}\right)\left(\frac{3y}{4}\right) + \left(\frac{3y}{4}\right)^{2}$$= \frac{4x^{2}}{9} + 2\left(\frac{6xy}{12}\right) + \frac{9y^{2}}{16}$$= \frac{4}{9}x^{2} + 2\left(\frac{xy}{2}\right) + \frac{9}{16}y^{2}$$= \frac{4}{9}x^{2} + xy + \frac{9}{16}y^{2}$.

Expand $\left(\frac{2x}{3} + \frac{3y}{4}\right)^{2}$.

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