Solve (x^2 2xy y^2) (3x^2 - xy^4y^2)

Question

Simplify the expression

6 x^{5} y^{3} - 2 x^{4} y^{9}

Evaluate

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

Remove the parentheses

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

Multiply

More Steps

Multiply the terms

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

Multiply the terms with the same base by adding their exponents

x y^{4 + 2}

Add the numbers

x y^{6}

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

Multiply the terms with the same base by adding their exponents

x^{2 + 1} \times 2 y \times y^{2} (3 x^{2} - x y^{6})

Add the numbers

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

Multiply the terms with the same base by adding their exponents

x^{3} \times 2 y^{1 + 2} (3 x^{2} - x y^{6})

Add the numbers

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

Use the commutative property to reorder the terms

2 x^{3} y^{3} (3 x^{2} - x y^{6})

Apply the distributive property

2 x^{3} y^{3} \times 3 x^{2} - 2 x^{3} y^{3} x y^{6}

Multiply the terms

More Steps

Evaluate

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

Multiply the numbers

6 x^{3} y^{3} x^{2}

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}

6 x^{5} y^{3}

6 x^{5} y^{3} - 2 x^{3} y^{3} x y^{6}

Solution

More Steps

Evaluate

2 x^{3} y^{3} x y^{6}

Multiply the terms

More Steps

Evaluate

x^{3} \times x

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

x^{3 + 1}

Add the numbers

x^{4}

2 x^{4} y^{3} \times y^{6}

Multiply the terms

More Steps

Evaluate

y^{3} \times y^{6}

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

y^{3 + 6}

Add the numbers

y^{9}

2 x^{4} y^{9}

6 x^{5} y^{3} - 2 x^{4} y^{9}

Show Solution

Factor the expression

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

Evaluate

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

Remove the parentheses

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

Multiply

More Steps

Multiply the terms

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

Multiply the terms with the same base by adding their exponents

x y^{4 + 2}

Add the numbers

x y^{6}

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

Multiply

More Steps

Multiply the terms

x^{2} \times 2 x y \times y^{2}

Multiply the terms with the same base by adding their exponents

x^{2 + 1} \times 2 y \times y^{2}

Add the numbers

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

Multiply the terms with the same base by adding their exponents

x^{3} \times 2 y^{1 + 2}

Add the numbers

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

Use the commutative property to reorder the terms

2 x^{3} y^{3}

2 x^{3} y^{3} (3 x^{2} - x y^{6})

Factor the expression

More Steps

Evaluate

3 x^{2} - x y^{6}

Rewrite the expression

x \times 3 x - x y^{6}

Factor out x from the expression

x (3 x - y^{6})

2 x^{3} y^{3} x (3 x - y^{6})

Solution

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

Show Solution