Pre-Algebra Examples

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

Step 1

Simplify and reorder the polynomial.

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Step 1.1

Rewrite ${(2 x + 8 y)}^{2}$ as $(2 x + 8 y) (2 x + 8 y)$ .

$(2 x + 8 y) (2 x + 8 y)$

Step 1.2

Expand $(2 x + 8 y) (2 x + 8 y)$ using the FOIL Method.

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Step 1.2.1

Apply the distributive property.

$2 x (2 x + 8 y) + 8 y (2 x + 8 y)$

Step 1.2.2

Apply the distributive property.

$2 x (2 x) + 2 x (8 y) + 8 y (2 x + 8 y)$

Step 1.2.3

Apply the distributive property.

$2 x (2 x) + 2 x (8 y) + 8 y (2 x) + 8 y (8 y)$

Step 1.3

Simplify and combine like terms.

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Step 1.3.1

Simplify each term.

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Step 1.3.1.1

Rewrite using the commutative property of multiplication.

$2 \cdot 2 x \cdot x + 2 x (8 y) + 8 y (2 x) + 8 y (8 y)$

Step 1.3.1.2

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

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Step 1.3.1.2.1

Move $x$ .

$2 \cdot 2 (x \cdot x) + 2 x (8 y) + 8 y (2 x) + 8 y (8 y)$

Step 1.3.1.2.2

Multiply $x$ by $x$ .

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

Step 1.3.1.3

Multiply $2$ by $2$ .

$4 x^{2} + 2 x (8 y) + 8 y (2 x) + 8 y (8 y)$

Step 1.3.1.4

Rewrite using the commutative property of multiplication.

$4 x^{2} + 2 \cdot 8 x y + 8 y (2 x) + 8 y (8 y)$

Step 1.3.1.5

Multiply $2$ by $8$ .

$4 x^{2} + 16 x y + 8 y (2 x) + 8 y (8 y)$

Step 1.3.1.6

Rewrite using the commutative property of multiplication.

$4 x^{2} + 16 x y + 8 \cdot 2 y x + 8 y (8 y)$

Step 1.3.1.7

Multiply $8$ by $2$ .

$4 x^{2} + 16 x y + 16 y x + 8 y (8 y)$

Step 1.3.1.8

Rewrite using the commutative property of multiplication.

$4 x^{2} + 16 x y + 16 y x + 8 \cdot 8 y \cdot y$

Step 1.3.1.9

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

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Step 1.3.1.9.1

Move $y$ .

$4 x^{2} + 16 x y + 16 y x + 8 \cdot 8 (y \cdot y)$

Step 1.3.1.9.2

Multiply $y$ by $y$ .

$4 x^{2} + 16 x y + 16 y x + 8 \cdot 8 y^{2}$

Step 1.3.1.10

Multiply $8$ by $8$ .

$4 x^{2} + 16 x y + 16 y x + 64 y^{2}$

Step 1.3.2

Add $16 x y$ and $16 y x$ .

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Step 1.3.2.1

Move $y$ .

$4 x^{2} + 16 x y + 16 x y + 64 y^{2}$

Step 1.3.2.2

Add $16 x y$ and $16 x y$ .

$4 x^{2} + 32 x y + 64 y^{2}$

Step 2

The largest exponent is the degree of the polynomial.

$2$