Solve ( 1/4 x -y)(x^(2) 4xy 16y^(2)) 4(4y^(3)- 1/16 x

Question

Simplify the expression

256 x^{4} y^{6} - 4 x^{7} y^{3} - 1024 x^{3} y^{7} + 16 x^{6} y^{4}

Evaluate

(\frac{1}{4} x - y) (x^{2} \times 4 x y \times 16 y^{2}) \times 4 (4 y^{3} - \frac{1}{16} x^{3} \times 1)

Remove the parentheses

(\frac{1}{4} x - y) x^{2} \times 4 x y \times 16 y^{2} \times 4 (4 y^{3} - \frac{1}{16} x^{3} \times 1)

Multiply the terms

(\frac{1}{4} x - y) x^{2} \times 4 x y \times 16 y^{2} \times 4 (4 y^{3} - \frac{1}{16} x^{3})

Multiply the terms with the same base by adding their exponents

(\frac{1}{4} x - y) x^{2 + 1} \times 4 y \times 16 y^{2} \times 4 (4 y^{3} - \frac{1}{16} x^{3})

Add the numbers

(\frac{1}{4} x - y) x^{3} \times 4 y \times 16 y^{2} \times 4 (4 y^{3} - \frac{1}{16} x^{3})

Multiply the terms

More Steps

(\frac{1}{4} x - y) x^{3} \times 256 y \times y^{2} (4 y^{3} - \frac{1}{16} x^{3})

Multiply the terms with the same base by adding their exponents

(\frac{1}{4} x - y) x^{3} \times 256 y^{1 + 2} (4 y^{3} - \frac{1}{16} x^{3})

Add the numbers

(\frac{1}{4} x - y) x^{3} \times 256 y^{3} (4 y^{3} - \frac{1}{16} x^{3})

Use the commutative property to reorder the terms

(\frac{1}{4} x - y) \times 256 x^{3} y^{3} (4 y^{3} - \frac{1}{16} x^{3})

Multiply the first two terms

256 x^{3} y^{3} (\frac{1}{4} x - y) (4 y^{3} - \frac{1}{16} x^{3})

Multiply the terms

More Steps

(64 x^{4} y^{3} - 256 x^{3} y^{4}) (4 y^{3} - \frac{1}{16} x^{3})

Apply the distributive property

64 x^{4} y^{3} \times 4 y^{3} - 64 x^{4} y^{3} \times \frac{1}{16} x^{3} - 256 x^{3} y^{4} \times 4 y^{3} - (- 256 x^{3} y^{4} \times \frac{1}{16} x^{3})

Multiply the terms

More Steps

256 x^{4} y^{6} - 64 x^{4} y^{3} \times \frac{1}{16} x^{3} - 256 x^{3} y^{4} \times 4 y^{3} - (- 256 x^{3} y^{4} \times \frac{1}{16} x^{3})

Multiply the terms

More Steps

256 x^{4} y^{6} - 4 x^{7} y^{3} - 256 x^{3} y^{4} \times 4 y^{3} - (- 256 x^{3} y^{4} \times \frac{1}{16} x^{3})

Multiply the terms

More Steps

256 x^{4} y^{6} - 4 x^{7} y^{3} - 1024 x^{3} y^{7} - (- 256 x^{3} y^{4} \times \frac{1}{16} x^{3})

Multiply the terms

More Steps

256 x^{4} y^{6} - 4 x^{7} y^{3} - 1024 x^{3} y^{7} - (- 16 x^{6} y^{4})

Solution

256 x^{4} y^{6} - 4 x^{7} y^{3} - 1024 x^{3} y^{7} + 16 x^{6} y^{4}

Show Solution

4 x^{3} y^{3} (x - 4 y) (16 y^{2} + 4 y x + x^{2}) (4 y - x)

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