Algebra Examples

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

Step 1

Simplify each term.

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Step 1.1

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

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Step 1.1.1

Apply the distributive property.

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

Step 1.1.2

Apply the distributive property.

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

Step 1.1.3

Apply the distributive property.

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

Step 1.2

Simplify and combine like terms.

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Step 1.2.1

Simplify each term.

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Step 1.2.1.1

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

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Step 1.2.1.1.1

Move $x$ .

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

Step 1.2.1.1.2

Multiply $x$ by $x$ .

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

Step 1.2.1.2

Rewrite using the commutative property of multiplication.

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

Step 1.2.1.3

Multiply $8$ by $- 8$ .

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

Step 1.2.1.4

Rewrite using the commutative property of multiplication.

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

Step 1.2.1.5

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

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Step 1.2.1.5.1

Move $y$ .

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

Step 1.2.1.5.2

Multiply $y$ by $y$ .

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

Step 1.2.2

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

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Step 1.2.2.1

Reorder $y$ and $x$ .

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

Step 1.2.2.2

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

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

Step 1.3

Apply the distributive property.

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

Step 1.4

Multiply $8$ by $- 1$ .

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

Step 1.5

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

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Step 1.5.1

Apply the distributive property.

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

Step 1.5.2

Apply the distributive property.

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

Step 1.5.3

Apply the distributive property.

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

Step 1.6

Simplify and combine like terms.

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Step 1.6.1

Simplify each term.

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Step 1.6.1.1

Rewrite using the commutative property of multiplication.

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

Step 1.6.1.2

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

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Step 1.6.1.2.1

Move $x$ .

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

Step 1.6.1.2.2

Multiply $x$ by $x$ .

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

Step 1.6.1.3

Multiply $- 1$ by $8$ .

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

Step 1.6.1.4

Rewrite using the commutative property of multiplication.

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

Step 1.6.1.5

Multiply $- 1$ by $- 1$ .

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

Step 1.6.1.6

Multiply $x$ by $1$ .

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

Step 1.6.1.7

Rewrite using the commutative property of multiplication.

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

Step 1.6.1.8

Multiply $- 8$ by $8$ .

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

Step 1.6.1.9

Rewrite using the commutative property of multiplication.

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

Step 1.6.1.10

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

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Step 1.6.1.10.1

Move $y$ .

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

Step 1.6.1.10.2

Multiply $y$ by $y$ .

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

Step 1.6.1.11

Multiply $- 8$ by $- 1$ .

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

Step 1.6.2

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

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Step 1.6.2.1

Move $y$ .

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

Step 1.6.2.2

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.

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Step 2.1

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

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Step 2.1.1

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

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

Step 2.1.2

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

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

Step 2.1.3

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

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

Step 2.1.4

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

$- 63 x y - 63 x y$

Step 2.2

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

$- 126 x y$