Solve (x-y)^8 * (x y) - ScanMath

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Question

Simplify the expression

x^{9} y - 8 x^{8} y^{2} + 28 x^{7} y^{3} - 56 x^{6} y^{4} + 70 x^{5} y^{5} - 56 x^{4} y^{6} + 28 x^{3} y^{7} - 8 x^{2} y^{8} + x y^{9}

Evaluate

(x - y)^{8} x y

Use the commutative property to reorder the terms

x y (x - y)^{8}

Expand the expression

x y (x^{8} - 8 x^{7} y + 28 x^{6} y^{2} - 56 x^{5} y^{3} + 70 x^{4} y^{4} - 56 x^{3} y^{5} + 28 x^{2} y^{6} - 8 x y^{7} + y^{8})

Apply the distributive property

x y x^{8} - x y \times 8 x^{7} y + x y \times 28 x^{6} y^{2} - x y \times 56 x^{5} y^{3} + x y \times 70 x^{4} y^{4} - x y \times 56 x^{3} y^{5} + x y \times 28 x^{2} y^{6} - x y \times 8 x y^{7} + x y \times y^{8}

Multiply the terms

More Steps

x^{9} y - x y \times 8 x^{7} y + x y \times 28 x^{6} y^{2} - x y \times 56 x^{5} y^{3} + x y \times 70 x^{4} y^{4} - x y \times 56 x^{3} y^{5} + x y \times 28 x^{2} y^{6} - x y \times 8 x y^{7} + x y \times y^{8}

Multiply the terms

More Steps

x^{9} y - 8 x^{8} y^{2} + x y \times 28 x^{6} y^{2} - x y \times 56 x^{5} y^{3} + x y \times 70 x^{4} y^{4} - x y \times 56 x^{3} y^{5} + x y \times 28 x^{2} y^{6} - x y \times 8 x y^{7} + x y \times y^{8}

Multiply the terms

More Steps

x^{9} y - 8 x^{8} y^{2} + 28 x^{7} y^{3} - x y \times 56 x^{5} y^{3} + x y \times 70 x^{4} y^{4} - x y \times 56 x^{3} y^{5} + x y \times 28 x^{2} y^{6} - x y \times 8 x y^{7} + x y \times y^{8}

Multiply the terms

More Steps

x^{9} y - 8 x^{8} y^{2} + 28 x^{7} y^{3} - 56 x^{6} y^{4} + x y \times 70 x^{4} y^{4} - x y \times 56 x^{3} y^{5} + x y \times 28 x^{2} y^{6} - x y \times 8 x y^{7} + x y \times y^{8}

Multiply the terms

More Steps

x^{9} y - 8 x^{8} y^{2} + 28 x^{7} y^{3} - 56 x^{6} y^{4} + 70 x^{5} y^{5} - x y \times 56 x^{3} y^{5} + x y \times 28 x^{2} y^{6} - x y \times 8 x y^{7} + x y \times y^{8}

Multiply the terms

More Steps

x^{9} y - 8 x^{8} y^{2} + 28 x^{7} y^{3} - 56 x^{6} y^{4} + 70 x^{5} y^{5} - 56 x^{4} y^{6} + x y \times 28 x^{2} y^{6} - x y \times 8 x y^{7} + x y \times y^{8}

Multiply the terms

More Steps

x^{9} y - 8 x^{8} y^{2} + 28 x^{7} y^{3} - 56 x^{6} y^{4} + 70 x^{5} y^{5} - 56 x^{4} y^{6} + 28 x^{3} y^{7} - x y \times 8 x y^{7} + x y \times y^{8}

Multiply the terms

More Steps

x^{9} y - 8 x^{8} y^{2} + 28 x^{7} y^{3} - 56 x^{6} y^{4} + 70 x^{5} y^{5} - 56 x^{4} y^{6} + 28 x^{3} y^{7} - 8 x^{2} y^{8} + x y \times y^{8}

Solution

More Steps

x^{9} y - 8 x^{8} y^{2} + 28 x^{7} y^{3} - 56 x^{6} y^{4} + 70 x^{5} y^{5} - 56 x^{4} y^{6} + 28 x^{3} y^{7} - 8 x^{2} y^{8} + x y^{9}

Show Solution