Solve (x^2y^2z)^2 (x-2y-2z)^2

Question

Simplify the expression

x^{6} y^{4} z^{2} - 4 x^{5} y^{5} z^{2} - 4 x^{5} y^{4} z^{3} + 4 x^{4} y^{6} z^{2} + 8 x^{4} y^{5} z^{3} + 4 x^{4} y^{4} z^{4}

Evaluate

(x^{2} y^{2} z)^{2} (x - 2 y - 2 z)^{2}

Evaluate the power

x^{4} y^{4} z^{2} (x - 2 y - 2 z)^{2}

Evaluate the power

x^{4} y^{4} z^{2} (x^{2} - 4 x y - 4 x z + 4 y^{2} + 8 yz + 4 z^{2})

Apply the distributive property

x^{4} y^{4} z^{2} x^{2} - x^{4} y^{4} z^{2} \times 4 x y - x^{4} y^{4} z^{2} \times 4 x z + x^{4} y^{4} z^{2} \times 4 y^{2} + x^{4} y^{4} z^{2} \times 8 yz + x^{4} y^{4} z^{2} \times 4 z^{2}

Multiply the terms

More Steps

x^{6} y^{4} z^{2} - x^{4} y^{4} z^{2} \times 4 x y - x^{4} y^{4} z^{2} \times 4 x z + x^{4} y^{4} z^{2} \times 4 y^{2} + x^{4} y^{4} z^{2} \times 8 yz + x^{4} y^{4} z^{2} \times 4 z^{2}

Multiply the terms

More Steps

x^{6} y^{4} z^{2} - 4 x^{5} y^{5} z^{2} - x^{4} y^{4} z^{2} \times 4 x z + x^{4} y^{4} z^{2} \times 4 y^{2} + x^{4} y^{4} z^{2} \times 8 yz + x^{4} y^{4} z^{2} \times 4 z^{2}

Multiply the terms

More Steps

x^{6} y^{4} z^{2} - 4 x^{5} y^{5} z^{2} - 4 x^{5} y^{4} z^{3} + x^{4} y^{4} z^{2} \times 4 y^{2} + x^{4} y^{4} z^{2} \times 8 yz + x^{4} y^{4} z^{2} \times 4 z^{2}

Multiply the terms

More Steps

x^{6} y^{4} z^{2} - 4 x^{5} y^{5} z^{2} - 4 x^{5} y^{4} z^{3} + 4 x^{4} y^{6} z^{2} + x^{4} y^{4} z^{2} \times 8 yz + x^{4} y^{4} z^{2} \times 4 z^{2}

Multiply the terms

More Steps

x^{6} y^{4} z^{2} - 4 x^{5} y^{5} z^{2} - 4 x^{5} y^{4} z^{3} + 4 x^{4} y^{6} z^{2} + 8 x^{4} y^{5} z^{3} + x^{4} y^{4} z^{2} \times 4 z^{2}

Solution

More Steps

x^{6} y^{4} z^{2} - 4 x^{5} y^{5} z^{2} - 4 x^{5} y^{4} z^{3} + 4 x^{4} y^{6} z^{2} + 8 x^{4} y^{5} z^{3} + 4 x^{4} y^{4} z^{4}

Show Solution