Solve (3/4x-2/5y)(3/4x+2/5y)=

$$( \frac { 3 } { 4 } x - \frac { 2 } { 5 } y ) ( \frac { 3 } { 4 } x + \frac { 2 } { 5 } y ) =$$

Evaluate

$$\frac{9x^{2}}{16}-\frac{4y^{2}}{25}$$

Solution Steps

Multiplication can be transformed into difference of squares using the rule: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}.

$$\left(\frac{3}{4}x\right)^{2}-\left(\frac{2}{5}y\right)^{2}$$

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

$$\left(\frac{3}{4}\right)^{2}x^{2}-\left(\frac{2}{5}y\right)^{2}$$

Calculate \frac{3}{4} to the power of 2 and get \frac{9}{16}.

$$\frac{9}{16}x^{2}-\left(\frac{2}{5}y\right)^{2}$$

Expand \left(\frac{2}{5}y\right)^{2}.

$$\frac{9}{16}x^{2}-\left(\frac{2}{5}\right)^{2}y^{2}$$

Calculate \frac{2}{5} to the power of 2 and get \frac{4}{25}.

$$\frac{9}{16}x^{2}-\frac{4}{25}y^{2}$$

Expand

$$\frac{9x^{2}}{16}-\frac{4y^{2}}{25}$$

Solution Steps

Multiplication can be transformed into difference of squares using the rule: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}.

$$\left(\frac{3}{4}x\right)^{2}-\left(\frac{2}{5}y\right)^{2}$$

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

$$\left(\frac{3}{4}\right)^{2}x^{2}-\left(\frac{2}{5}y\right)^{2}$$

Calculate \frac{3}{4} to the power of 2 and get \frac{9}{16}.

$$\frac{9}{16}x^{2}-\left(\frac{2}{5}y\right)^{2}$$

Expand \left(\frac{2}{5}y\right)^{2}.

$$\frac{9}{16}x^{2}-\left(\frac{2}{5}\right)^{2}y^{2}$$

Calculate \frac{2}{5} to the power of 2 and get \frac{4}{25}.

$$\frac{9}{16}x^{2}-\frac{4}{25}y^{2}$$