Simplify (8x+y)(x-8y)-(x+8y)(8x-y)

$(8 x + y) (x - 8 y) - (x + 8 y) (8 x - y)$

Step 1

Simplify each term.

Expand $(8 x + y) (x - 8 y)$ using the FOIL Method.

Apply the distributive property.

$8 x (x - 8 y) + y (x - 8 y) - (x + 8 y) (8 x - y)$

Apply the distributive property.

$8 x \cdot x + 8 x (- 8 y) + y (x - 8 y) - (x + 8 y) (8 x - y)$

Apply the distributive property.

$8 x \cdot x + 8 x (- 8 y) + y x + y (- 8 y) - (x + 8 y) (8 x - y)$

Simplify and combine like terms.

Simplify each term.

Multiply $x$ by $x$ by adding the exponents.

Move $x$ .

$8 (x \cdot x) + 8 x (- 8 y) + y x + y (- 8 y) - (x + 8 y) (8 x - y)$

Multiply $x$ by $x$ .

$8 x^{2} + 8 x (- 8 y) + y x + y (- 8 y) - (x + 8 y) (8 x - y)$

Rewrite using the commutative property of multiplication.

$8 x^{2} + 8 \cdot - 8 x y + y x + y (- 8 y) - (x + 8 y) (8 x - y)$

Multiply $8$ by $- 8$ .

$8 x^{2} - 64 x y + y x + y (- 8 y) - (x + 8 y) (8 x - y)$

Rewrite using the commutative property of multiplication.

$8 x^{2} - 64 x y + y x - 8 y \cdot y - (x + 8 y) (8 x - y)$

Multiply $y$ by $y$ by adding the exponents.

Move $y$ .

$8 x^{2} - 64 x y + y x - 8 (y \cdot y) - (x + 8 y) (8 x - y)$

Multiply $y$ by $y$ .

$8 x^{2} - 64 x y + y x - 8 y^{2} - (x + 8 y) (8 x - y)$

Add $- 64 x y$ and $y x$ .

Reorder $y$ and $x$ .

$8 x^{2} - 64 x y + x y - 8 y^{2} - (x + 8 y) (8 x - y)$

Add $- 64 x y$ and $x y$ .

$8 x^{2} - 63 x y - 8 y^{2} - (x + 8 y) (8 x - y)$

Apply the distributive property.

$8 x^{2} - 63 x y - 8 y^{2} + (- x - (8 y)) (8 x - y)$

Multiply $8$ by $- 1$ .

$8 x^{2} - 63 x y - 8 y^{2} + (- x - 8 y) (8 x - y)$

Expand $(- x - 8 y) (8 x - y)$ using the FOIL Method.

Apply the distributive property.

$8 x^{2} - 63 x y - 8 y^{2} - x (8 x - y) - 8 y (8 x - y)$

Apply the distributive property.

$8 x^{2} - 63 x y - 8 y^{2} - x (8 x) - x (- y) - 8 y (8 x - y)$

Apply the distributive property.

$8 x^{2} - 63 x y - 8 y^{2} - x (8 x) - x (- y) - 8 y (8 x) - 8 y (- y)$

Simplify and combine like terms.

Simplify each term.

Rewrite using the commutative property of multiplication.

$8 x^{2} - 63 x y - 8 y^{2} - 1 \cdot 8 x \cdot x - x (- y) - 8 y (8 x) - 8 y (- y)$

Multiply $x$ by $x$ by adding the exponents.

Move $x$ .

$8 x^{2} - 63 x y - 8 y^{2} - 1 \cdot 8 (x \cdot x) - x (- y) - 8 y (8 x) - 8 y (- y)$

Multiply $x$ by $x$ .

$8 x^{2} - 63 x y - 8 y^{2} - 1 \cdot 8 x^{2} - x (- y) - 8 y (8 x) - 8 y (- y)$

Multiply $- 1$ by $8$ .

$8 x^{2} - 63 x y - 8 y^{2} - 8 x^{2} - x (- y) - 8 y (8 x) - 8 y (- y)$

Rewrite using the commutative property of multiplication.

$8 x^{2} - 63 x y - 8 y^{2} - 8 x^{2} - 1 \cdot - 1 x y - 8 y (8 x) - 8 y (- y)$

Multiply $- 1$ by $- 1$ .

$8 x^{2} - 63 x y - 8 y^{2} - 8 x^{2} + 1 x y - 8 y (8 x) - 8 y (- y)$

Multiply $x$ by $1$ .

$8 x^{2} - 63 x y - 8 y^{2} - 8 x^{2} + x y - 8 y (8 x) - 8 y (- y)$

Rewrite using the commutative property of multiplication.

$8 x^{2} - 63 x y - 8 y^{2} - 8 x^{2} + x y - 8 \cdot 8 y x - 8 y (- y)$

Multiply $- 8$ by $8$ .

$8 x^{2} - 63 x y - 8 y^{2} - 8 x^{2} + x y - 64 y x - 8 y (- y)$

Rewrite using the commutative property of multiplication.

$8 x^{2} - 63 x y - 8 y^{2} - 8 x^{2} + x y - 64 y x - 8 \cdot - 1 y \cdot y$

Multiply $y$ by $y$ by adding the exponents.

Move $y$ .

$8 x^{2} - 63 x y - 8 y^{2} - 8 x^{2} + x y - 64 y x - 8 \cdot - 1 (y \cdot y)$

Multiply $y$ by $y$ .

$8 x^{2} - 63 x y - 8 y^{2} - 8 x^{2} + x y - 64 y x - 8 \cdot - 1 y^{2}$

Multiply $- 8$ by $- 1$ .

$8 x^{2} - 63 x y - 8 y^{2} - 8 x^{2} + x y - 64 y x + 8 y^{2}$

Subtract $64 y x$ from $x y$ .

Move $y$ .

$8 x^{2} - 63 x y - 8 y^{2} - 8 x^{2} + x y - 64 x y + 8 y^{2}$

Subtract $64 x y$ from $x y$ .

$8 x^{2} - 63 x y - 8 y^{2} - 8 x^{2} - 63 x y + 8 y^{2}$

Step 2

Simplify by adding terms.

Combine the opposite terms in $8 x^{2} - 63 x y - 8 y^{2} - 8 x^{2} - 63 x y + 8 y^{2}$ .

Subtract $8 x^{2}$ from $8 x^{2}$ .

$- 63 x y - 8 y^{2} + 0 - 63 x y + 8 y^{2}$

Add $- 63 x y - 8 y^{2}$ and $0$ .

$- 63 x y - 8 y^{2} - 63 x y + 8 y^{2}$

Add $- 8 y^{2}$ and $8 y^{2}$ .

$- 63 x y - 63 x y + 0$

Add $- 63 x y - 63 x y$ and $0$ .

$- 63 x y - 63 x y$

Subtract $63 x y$ from $- 63 x y$ .

$- 126 x y$

Simplify (8x+y)(x-8y)-(x+8y)(8x-y)

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