Solve 1/4x^2-2xy+4y^2-9/4y^2-9x^2-9xy

$$\frac { 1 } { 4 } x ^ { 2 } - 2 x y + 4 y ^ { 2 } - \frac { 9 } { 4 } y ^ { 2 } - 9 x ^ { 2 } - 9 x y$$

Evaluate

$$\frac{\left(y-7x\right)\left(5x+7y\right)}{4}$$

Solution Steps

Combine 4y^{2} and -\frac{9}{4}y^{2} to get \frac{7}{4}y^{2}.

$$\frac{1}{4}x^{2}-2xy+\frac{7}{4}y^{2}-9x^{2}-9xy$$

Combine \frac{1}{4}x^{2} and -9x^{2} to get -\frac{35}{4}x^{2}.

$$-\frac{35}{4}x^{2}-2xy+\frac{7}{4}y^{2}-9xy$$

Combine -2xy and -9xy to get -11xy.

$$-\frac{35}{4}x^{2}-11xy+\frac{7}{4}y^{2}$$

Factor

$$\frac{\left(y-7x\right)\left(5x+7y\right)}{4}$$

Solution Steps

Factor out \frac{1}{4}.

$$\frac{x^{2}-8xy+16y^{2}-9y^{2}-36x^{2}-36xy}{4}$$

Consider x^{2}-8xy+16y^{2}-9y^{2}-36x^{2}-36xy. Multiply and combine like terms.

$$-35x^{2}-44xy+7y^{2}$$

Consider -35x^{2}-44xy+7y^{2}. Consider -35x^{2}-44xy+7y^{2} as a polynomial over variable x.

$$-35x^{2}-44yx+7y^{2}$$

Find one factor of the form kx^{m}+n, where kx^{m} divides the monomial with the highest power -35x^{2} and n divides the constant factor 7y^{2}. One such factor is 5x+7y. Factor the polynomial by dividing it by this factor.

$$\left(5x+7y\right)\left(-7x+y\right)$$

Rewrite the complete factored expression.

$$\frac{\left(5x+7y\right)\left(-7x+y\right)}{4}$$