Expand the Trigonometric Expression (x+8y)^2

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

Step 1

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

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

Step 2

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

Apply the distributive property.

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

Apply the distributive property.

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

Apply the distributive property.

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

Step 3

Simplify and combine like terms.

Simplify each term.

Multiply $x$ by $x$ .

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

Rewrite using the commutative property of multiplication.

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

Rewrite using the commutative property of multiplication.

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

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

Move $y$ .

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

Multiply $y$ by $y$ .

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

Multiply $8$ by $8$ .

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

Add $8 x y$ and $8 y x$ .

Move $y$ .

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

Add $8 x y$ and $8 x y$ .

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