Solve 3x^2-4y+3a^2x^2-4a^2y

$$3 x ^ { 2 } - 4 y + 3 a ^ { 2 } x ^ { 2 } - 4 a ^ { 2 } y$$

Factor

$$\left(3x^{2}-4y\right)\left(a^{2}+1\right)$$

Solution Steps

Do the grouping 3x^{2}-4y+3a^{2}x^{2}-4a^{2}y=\left(3x^{2}-4y\right)+\left(3a^{2}x^{2}-4a^{2}y\right), and factor out a^{2} in 3a^{2}x^{2}-4a^{2}y.

$$3x^{2}-4y+a^{2}\left(3x^{2}-4y\right)$$

Factor out common term 3x^{2}-4y by using distributive property. Polynomial a^{2}+1 is not factored since it does not have any rational roots.

$$\left(3x^{2}-4y\right)\left(1+a^{2}\right)$$

Evaluate

$$\left(3x^{2}-4y\right)\left(a^{2}+1\right)$$