Solve -((x 1)^2 (y^2)^2 ((x-1)^2 (y-2)^2))

Question

Simplify the expression

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

Evaluate

- ((x \times 1)^{2} (y^{2})^{2} ((x - 1)^{2} (y - 2)^{2}))

Remove the parentheses

- ((x \times 1)^{2} (y^{2})^{2} (x - 1)^{2} (y - 2)^{2})

Multiply the exponents

- ((x \times 1)^{2} y^{2 \times 2} (x - 1)^{2} (y - 2)^{2})

Any expression multiplied by 1 remains the same

- (x^{2} y^{2 \times 2} (x - 1)^{2} (y - 2)^{2})

Multiply the numbers

- (x^{2} y^{4} (x - 1)^{2} (y - 2)^{2})

Calculate

- x^{2} y^{4} (x - 1)^{2} (y - 2)^{2}

Expand the expression

More Steps

- x^{2} y^{4} (x^{2} - 2 x + 1) (y - 2)^{2}

Expand the expression

More Steps

- x^{2} y^{4} (x^{2} - 2 x + 1) (y^{2} - 4 y + 4)

Multiply the terms

More Steps

(- x^{4} y^{4} + 2 x^{3} y^{4} - x^{2} y^{4}) (y^{2} - 4 y + 4)

Apply the distributive property

- x^{4} y^{4} \times y^{2} - (- x^{4} y^{4} \times 4 y) - x^{4} y^{4} \times 4 + 2 x^{3} y^{4} \times y^{2} - 2 x^{3} y^{4} \times 4 y + 2 x^{3} y^{4} \times 4 - x^{2} y^{4} \times y^{2} - (- x^{2} y^{4} \times 4 y) - x^{2} y^{4} \times 4

Multiply the terms

More Steps

- x^{4} y^{6} - (- x^{4} y^{4} \times 4 y) - x^{4} y^{4} \times 4 + 2 x^{3} y^{4} \times y^{2} - 2 x^{3} y^{4} \times 4 y + 2 x^{3} y^{4} \times 4 - x^{2} y^{4} \times y^{2} - (- x^{2} y^{4} \times 4 y) - x^{2} y^{4} \times 4

Multiply the terms

More Steps

- x^{4} y^{6} - (- 4 x^{4} y^{5}) - x^{4} y^{4} \times 4 + 2 x^{3} y^{4} \times y^{2} - 2 x^{3} y^{4} \times 4 y + 2 x^{3} y^{4} \times 4 - x^{2} y^{4} \times y^{2} - (- x^{2} y^{4} \times 4 y) - x^{2} y^{4} \times 4

Use the commutative property to reorder the terms

- x^{4} y^{6} - (- 4 x^{4} y^{5}) - 4 x^{4} y^{4} + 2 x^{3} y^{4} \times y^{2} - 2 x^{3} y^{4} \times 4 y + 2 x^{3} y^{4} \times 4 - x^{2} y^{4} \times y^{2} - (- x^{2} y^{4} \times 4 y) - x^{2} y^{4} \times 4

Multiply the terms

More Steps

- x^{4} y^{6} - (- 4 x^{4} y^{5}) - 4 x^{4} y^{4} + 2 x^{3} y^{6} - 2 x^{3} y^{4} \times 4 y + 2 x^{3} y^{4} \times 4 - x^{2} y^{4} \times y^{2} - (- x^{2} y^{4} \times 4 y) - x^{2} y^{4} \times 4

Multiply the terms

More Steps

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

Multiply the numbers

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

Multiply the terms

More Steps

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

Multiply the terms

More Steps

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

Use the commutative property to reorder the terms

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

Solution

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

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