Solve 64x^{4}y^{8}-160x^5y^5+100x^6y^2

$$64 x ^ { 4 } y ^ { 8 } - 160 x ^ { 5 } y ^ { 5 } + 100 x ^ { 6 } y ^ { 2 }$$

Factor

$$4y^{2}x^{4}\left(4y^{3}-5x\right)^{2}$$

Solution Steps

Factor out 4.

$$4\left(16x^{4}y^{8}-40x^{5}y^{5}+25x^{6}y^{2}\right)$$

Consider 16x^{4}y^{8}-40x^{5}y^{5}+25x^{6}y^{2}. Factor out x^{4}y^{2}.

$$x^{4}y^{2}\left(16y^{6}-40xy^{3}+25x^{2}\right)$$

Consider 16y^{6}-40xy^{3}+25x^{2}. Use the perfect square formula, a^{2}+2ab+b^{2}=\left(a+b\right)^{2}, where a=-5x and b=4y^{3}.

$$\left(-5x+4y^{3}\right)^{2}$$

Rewrite the complete factored expression.

$$4x^{4}y^{2}\left(-5x+4y^{3}\right)^{2}$$

Evaluate

$$4x^{4}\left(y\left(4y^{3}-5x\right)\right)^{2}$$