Solve x^2 xy^2 5(3y - 2x) 2(2x-3y) x^2 y^2

Question

Simplify the expression

- 90 x^{5} y^{6} + 120 x^{6} y^{5} - 40 x^{7} y^{4}

Evaluate

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

Multiply the terms with the same base by adding their exponents

x^{2 + 1 + 2} y^{2} \times 5 (3 y - 2 x) \times 2 (2 x - 3 y) y^{2}

Add the numbers

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

Multiply the terms with the same base by adding their exponents

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

Add the numbers

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

Multiply the terms

x^{5} y^{4} \times 10 (3 y - 2 x) (2 x - 3 y)

Use the commutative property to reorder the terms

10 x^{5} y^{4} (3 y - 2 x) (2 x - 3 y)

Multiply the terms

10 x^{5} y^{4} (- (3 y - 2 x)^{2})

Use the commutative property to reorder the terms

x^{5} y^{4} (- 10) (3 y - 2 x)^{2}

Use the commutative property to reorder the terms

- 10 x^{5} y^{4} (3 y - 2 x)^{2}

Expand the expression

More Steps

- 10 x^{5} y^{4} (9 y^{2} - 12 y x + 4 x^{2})

Apply the distributive property

- 10 x^{5} y^{4} \times 9 y^{2} - (- 10 x^{5} y^{4} \times 12 y x) - 10 x^{5} y^{4} \times 4 x^{2}

Multiply the terms

More Steps

- 90 x^{5} y^{6} - (- 10 x^{5} y^{4} \times 12 y x) - 10 x^{5} y^{4} \times 4 x^{2}

Multiply the terms

More Steps

- 90 x^{5} y^{6} - (- 120 x^{6} y^{5}) - 10 x^{5} y^{4} \times 4 x^{2}

Multiply the terms

More Steps

- 90 x^{5} y^{6} - (- 120 x^{6} y^{5}) - 40 x^{7} y^{4}

Solution

- 90 x^{5} y^{6} + 120 x^{6} y^{5} - 40 x^{7} y^{4}

Show Solution