Solve 225x^{4}+25m^2n^4-150x^2mn^2

$$225 x ^ { 4 } + 25 m ^ { 2 } n ^ { 4 } - 150 x ^ { 2 } m n ^ { 2 }$$

Factor

$$25\left(3x^{2}-mn^{2}\right)^{2}$$

Solution Steps

Factor out 25.

$$25\left(9x^{4}+m^{2}n^{4}-6x^{2}mn^{2}\right)$$

Consider 9x^{4}+m^{2}n^{4}-6x^{2}mn^{2}. Use the perfect square formula, a^{2}-2ab+b^{2}=\left(a-b\right)^{2}, where a=3x^{2} and b=mn^{2}.

$$\left(3x^{2}-mn^{2}\right)^{2}$$

Rewrite the complete factored expression.

$$25\left(3x^{2}-mn^{2}\right)^{2}$$

Evaluate

$$25\left(3x^{2}-mn^{2}\right)^{2}$$