Solve 9x^2/49-12xydiv35+4y^2/25

$$\frac{ 9 { x }^{ 2 } }{ 49 } -12xy \div 35+ \frac{ 4 { y }^{ 2 } }{ 25 }$$

Evaluate

$$\frac{\left(15x-14y\right)^{2}}{1225}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 49 and 35 is 245. Multiply \frac{9x^{2}}{49} times \frac{5}{5}. Multiply \frac{12xy}{35} times \frac{7}{7}.

$$\frac{5\times 9x^{2}}{245}-\frac{7\times 12xy}{245}+\frac{4y^{2}}{25}$$

Since \frac{5\times 9x^{2}}{245} and \frac{7\times 12xy}{245} have the same denominator, subtract them by subtracting their numerators.

$$\frac{5\times 9x^{2}-7\times 12xy}{245}+\frac{4y^{2}}{25}$$

Do the multiplications in 5\times 9x^{2}-7\times 12xy.

$$\frac{45x^{2}-84xy}{245}+\frac{4y^{2}}{25}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 245 and 25 is 1225. Multiply \frac{45x^{2}-84xy}{245} times \frac{5}{5}. Multiply \frac{4y^{2}}{25} times \frac{49}{49}.

$$\frac{5\left(45x^{2}-84xy\right)}{1225}+\frac{49\times 4y^{2}}{1225}$$

Since \frac{5\left(45x^{2}-84xy\right)}{1225} and \frac{49\times 4y^{2}}{1225} have the same denominator, add them by adding their numerators.

$$\frac{5\left(45x^{2}-84xy\right)+49\times 4y^{2}}{1225}$$

Do the multiplications in 5\left(45x^{2}-84xy\right)+49\times 4y^{2}.

$$\frac{225x^{2}-420xy+196y^{2}}{1225}$$

Factor

$$\frac{\left(15x-14y\right)^{2}}{1225}$$

Solution Steps

Factor out \frac{1}{1225}.

$$\frac{225x^{2}-420xy+196y^{2}}{1225}$$

Consider 225x^{2}-420xy+196y^{2}. Use the perfect square formula, a^{2}-2ab+b^{2}=\left(a-b\right)^{2}, where a=15x and b=14y.

$$\left(15x-14y\right)^{2}$$

Rewrite the complete factored expression.

$$\frac{\left(15x-14y\right)^{2}}{1225}$$