Solve 25x^2/4+20xy/3+16y^2/9=

$$\frac { 25 x ^ { 2 } } { 4 } + \frac { 20 x y } { 3 } + \frac { 16 y ^ { 2 } } { 9 } =$$

Evaluate

$$\frac{\left(15x+8y\right)^{2}}{36}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 4 and 3 is 12. Multiply \frac{25x^{2}}{4} times \frac{3}{3}. Multiply \frac{20xy}{3} times \frac{4}{4}.

$$\frac{3\times 25x^{2}}{12}+\frac{4\times 20xy}{12}+\frac{16y^{2}}{9}$$

Since \frac{3\times 25x^{2}}{12} and \frac{4\times 20xy}{12} have the same denominator, add them by adding their numerators.

$$\frac{3\times 25x^{2}+4\times 20xy}{12}+\frac{16y^{2}}{9}$$

Do the multiplications in 3\times 25x^{2}+4\times 20xy.

$$\frac{75x^{2}+80xy}{12}+\frac{16y^{2}}{9}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 12 and 9 is 36. Multiply \frac{75x^{2}+80xy}{12} times \frac{3}{3}. Multiply \frac{16y^{2}}{9} times \frac{4}{4}.

$$\frac{3\left(75x^{2}+80xy\right)}{36}+\frac{4\times 16y^{2}}{36}$$

Since \frac{3\left(75x^{2}+80xy\right)}{36} and \frac{4\times 16y^{2}}{36} have the same denominator, add them by adding their numerators.

$$\frac{3\left(75x^{2}+80xy\right)+4\times 16y^{2}}{36}$$

Do the multiplications in 3\left(75x^{2}+80xy\right)+4\times 16y^{2}.

$$\frac{225x^{2}+240xy+64y^{2}}{36}$$

Factor

$$\frac{\left(15x+8y\right)^{2}}{36}$$

Solution Steps

Factor out \frac{1}{36}.

$$\frac{225x^{2}+240xy+64y^{2}}{36}$$

Consider 225x^{2}+240xy+64y^{2}. Use the perfect square formula, a^{2}+2ab+b^{2}=\left(a+b\right)^{2}, where a=15x and b=8y.

$$\left(15x+8y\right)^{2}$$

Rewrite the complete factored expression.

$$\frac{\left(15x+8y\right)^{2}}{36}$$