Solve (x^3y)(x^2-3xy 9y^2)-3y(x^3y)(x-3y)*(3xy-7x 7)

Question

Simplify the expression

x^{5} y - 9 y^{3} x^{5} + 147 y^{2} x^{5} - 441 y^{3} x^{4}

Evaluate

x^{3} y (x^{2} - 3 x y \times 9 y^{2}) - 3 y x^{3} y (x - 3 y) (3 x y - 7 x \times 7)

Multiply

More Steps

Multiply the terms

3 x y \times 9 y^{2}

Multiply the terms

27 x y \times y^{2}

Multiply the terms with the same base by adding their exponents

27 x y^{1 + 2}

Add the numbers

27 x y^{3}

x^{3} y (x^{2} - 27 x y^{3}) - 3 y x^{3} y (x - 3 y) (3 x y - 7 x \times 7)

Multiply the terms

x^{3} y (x^{2} - 27 x y^{3}) - 3 y x^{3} y (x - 3 y) (3 x y - 49 x)

Multiply the terms

x^{3} y (x^{2} - 27 x y^{3}) - 3 y^{2} x^{3} (x - 3 y) (3 x y - 49 x)

Expand the expression

More Steps

Calculate

x^{3} y (x^{2} - 27 x y^{3})

Apply the distributive property

x^{3} y x^{2} - x^{3} y \times 27 x y^{3}

Multiply the terms

More Steps

Evaluate

x^{3} \times x^{2}

Use the product rule a^{n} \times a^{m} = a^{n + m} to simplify the expression

x^{3 + 2}

Add the numbers

x^{5}

x^{5} y - x^{3} y \times 27 x y^{3}

Multiply the terms

More Steps

Evaluate

x^{3} y \times 27 x y^{3}

Use the commutative property to reorder the terms

27 x^{3} y x y^{3}

Multiply the terms

27 x^{4} y \times y^{3}

Multiply the terms

27 x^{4} y^{4}

x^{5} y - 27 x^{4} y^{4}

x^{5} y - 27 x^{4} y^{4} - 3 y^{2} x^{3} (x - 3 y) (3 x y - 49 x)

Expand the expression

More Steps

Calculate

- 3 y^{2} x^{3} (x - 3 y) (3 x y - 49 x)

Simplify

More Steps

Evaluate

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

Apply the distributive property

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

Multiply the terms

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

Multiply the terms

- 3 y^{2} x^{4} - (- 9 y^{3} x^{3})

If a negative sign or a subtraction symbol appears outside parentheses, remove the parentheses and change the sign of every term within the parentheses

- 3 y^{2} x^{4} + 9 y^{3} x^{3}

(- 3 y^{2} x^{4} + 9 y^{3} x^{3}) (3 x y - 49 x)

Apply the distributive property

- 3 y^{2} x^{4} \times 3 x y - (- 3 y^{2} x^{4} \times 49 x) + 9 y^{3} x^{3} \times 3 x y - 9 y^{3} x^{3} \times 49 x

Multiply the terms

More Steps

Evaluate

- 3 y^{2} x^{4} \times 3 x y

Multiply the numbers

- 9 y^{2} x^{4} \times x y

Multiply the terms

- 9 y^{2} x^{5} y

Multiply the terms

- 9 y^{3} x^{5}

- 9 y^{3} x^{5} - (- 3 y^{2} x^{4} \times 49 x) + 9 y^{3} x^{3} \times 3 x y - 9 y^{3} x^{3} \times 49 x

Multiply the terms

More Steps

Evaluate

- 3 y^{2} x^{4} \times 49 x

Multiply the numbers

- 147 y^{2} x^{4} \times x

Multiply the terms

- 147 y^{2} x^{5}

- 9 y^{3} x^{5} - (- 147 y^{2} x^{5}) + 9 y^{3} x^{3} \times 3 x y - 9 y^{3} x^{3} \times 49 x

Multiply the terms

More Steps

Evaluate

9 y^{3} x^{3} \times 3 x y

Multiply the numbers

27 y^{3} x^{3} \times x y

Multiply the terms

27 y^{3} x^{4} y

Multiply the terms

27 y^{4} x^{4}

- 9 y^{3} x^{5} - (- 147 y^{2} x^{5}) + 27 y^{4} x^{4} - 9 y^{3} x^{3} \times 49 x

Multiply the terms

More Steps

Evaluate

9 y^{3} x^{3} \times 49 x

Multiply the numbers

441 y^{3} x^{3} \times x

Multiply the terms

441 y^{3} x^{4}

- 9 y^{3} x^{5} - (- 147 y^{2} x^{5}) + 27 y^{4} x^{4} - 441 y^{3} x^{4}

If a negative sign or a subtraction symbol appears outside parentheses, remove the parentheses and change the sign of every term within the parentheses

- 9 y^{3} x^{5} + 147 y^{2} x^{5} + 27 y^{4} x^{4} - 441 y^{3} x^{4}

x^{5} y - 27 x^{4} y^{4} - 9 y^{3} x^{5} + 147 y^{2} x^{5} + 27 y^{4} x^{4} - 441 y^{3} x^{4}

Add the terms

More Steps

Evaluate

- 27 x^{4} y^{4} + 27 y^{4} x^{4}

Rewrite the expression

- 27 x^{4} y^{4} + 27 x^{4} y^{4}

Collect like terms by calculating the sum or difference of their coefficients

(- 27 + 27) x^{4} y^{4}

Add the numbers

0 \times x^{4} y^{4}

Any expression multiplied by 0 equals 0

0

x^{5} y + 0 - 9 y^{3} x^{5} + 147 y^{2} x^{5} - 441 y^{3} x^{4}

Solution

x^{5} y - 9 y^{3} x^{5} + 147 y^{2} x^{5} - 441 y^{3} x^{4}

Show Solution

Factor the expression

x^{4} y (x - 9 y^{2} x + 147 y x - 441 y^{2})

Evaluate

x^{3} y (x^{2} - 3 x y \times 9 y^{2}) - 3 y x^{3} y (x - 3 y) (3 x y - 7 x \times 7)

Multiply

More Steps

Multiply the terms

3 x y \times 9 y^{2}

Multiply the terms

27 x y \times y^{2}

Multiply the terms with the same base by adding their exponents

27 x y^{1 + 2}

Add the numbers

27 x y^{3}

x^{3} y (x^{2} - 27 x y^{3}) - 3 y x^{3} y (x - 3 y) (3 x y - 7 x \times 7)

Multiply the terms

x^{3} y (x^{2} - 27 x y^{3}) - 3 y x^{3} y (x - 3 y) (3 x y - 49 x)

Multiply the terms

x^{3} y (x^{2} - 27 x y^{3}) - 3 y^{2} x^{3} (x - 3 y) (3 x y - 49 x)

Rewrite the expression

x^{4} y (x - 27 y^{3}) - x^{4} y \times 3 y (x - 3 y) (3 y - 49)

Factor out x^{4} y from the expression

x^{4} y (x - 27 y^{3} - 3 y (x - 3 y) (3 y - 49))

Solution

x^{4} y (x - 9 y^{2} x + 147 y x - 441 y^{2})

Show Solution