Find the Product (2x+3y+5)^2

${(2 x + 3 y + 5)}^{2}$

Rewrite ${(2 x + 3 y + 5)}^{2}$ as $(2 x + 3 y + 5) (2 x + 3 y + 5)$ .

$(2 x + 3 y + 5) (2 x + 3 y + 5)$

Expand $(2 x + 3 y + 5) (2 x + 3 y + 5)$ by multiplying each term in the first expression by each term in the second expression.

$2 x (2 x) + 2 x (3 y) + 2 x \cdot 5 + 3 y (2 x) + 3 y (3 y) + 3 y \cdot 5 + 5 (2 x) + 5 (3 y) + 5 \cdot 5$

Simplify each term.

Rewrite using the commutative property of multiplication.

$2 \cdot 2 x \cdot x + 2 x (3 y) + 2 x \cdot 5 + 3 y (2 x) + 3 y (3 y) + 3 y \cdot 5 + 5 (2 x) + 5 (3 y) + 5 \cdot 5$

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

Move $x$ .

$2 \cdot 2 (x \cdot x) + 2 x (3 y) + 2 x \cdot 5 + 3 y (2 x) + 3 y (3 y) + 3 y \cdot 5 + 5 (2 x) + 5 (3 y) + 5 \cdot 5$

Multiply $x$ by $x$ .

$2 \cdot 2 x^{2} + 2 x (3 y) + 2 x \cdot 5 + 3 y (2 x) + 3 y (3 y) + 3 y \cdot 5 + 5 (2 x) + 5 (3 y) + 5 \cdot 5$

Multiply $2$ by $2$ .

$4 x^{2} + 2 x (3 y) + 2 x \cdot 5 + 3 y (2 x) + 3 y (3 y) + 3 y \cdot 5 + 5 (2 x) + 5 (3 y) + 5 \cdot 5$

Rewrite using the commutative property of multiplication.

$4 x^{2} + 2 \cdot 3 x y + 2 x \cdot 5 + 3 y (2 x) + 3 y (3 y) + 3 y \cdot 5 + 5 (2 x) + 5 (3 y) + 5 \cdot 5$

Multiply $2$ by $3$ .

$4 x^{2} + 6 x y + 2 x \cdot 5 + 3 y (2 x) + 3 y (3 y) + 3 y \cdot 5 + 5 (2 x) + 5 (3 y) + 5 \cdot 5$

Multiply $5$ by $2$ .

$4 x^{2} + 6 x y + 10 x + 3 y (2 x) + 3 y (3 y) + 3 y \cdot 5 + 5 (2 x) + 5 (3 y) + 5 \cdot 5$

Rewrite using the commutative property of multiplication.

$4 x^{2} + 6 x y + 10 x + 3 \cdot 2 y x + 3 y (3 y) + 3 y \cdot 5 + 5 (2 x) + 5 (3 y) + 5 \cdot 5$

Multiply $3$ by $2$ .

$4 x^{2} + 6 x y + 10 x + 6 y x + 3 y (3 y) + 3 y \cdot 5 + 5 (2 x) + 5 (3 y) + 5 \cdot 5$

Rewrite using the commutative property of multiplication.

$4 x^{2} + 6 x y + 10 x + 6 y x + 3 \cdot 3 y \cdot y + 3 y \cdot 5 + 5 (2 x) + 5 (3 y) + 5 \cdot 5$

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

Move $y$ .

$4 x^{2} + 6 x y + 10 x + 6 y x + 3 \cdot 3 (y \cdot y) + 3 y \cdot 5 + 5 (2 x) + 5 (3 y) + 5 \cdot 5$

Multiply $y$ by $y$ .

$4 x^{2} + 6 x y + 10 x + 6 y x + 3 \cdot 3 y^{2} + 3 y \cdot 5 + 5 (2 x) + 5 (3 y) + 5 \cdot 5$

Multiply $3$ by $3$ .

$4 x^{2} + 6 x y + 10 x + 6 y x + 9 y^{2} + 3 y \cdot 5 + 5 (2 x) + 5 (3 y) + 5 \cdot 5$

Multiply $5$ by $3$ .

$4 x^{2} + 6 x y + 10 x + 6 y x + 9 y^{2} + 15 y + 5 (2 x) + 5 (3 y) + 5 \cdot 5$

Multiply $2$ by $5$ .

$4 x^{2} + 6 x y + 10 x + 6 y x + 9 y^{2} + 15 y + 10 x + 5 (3 y) + 5 \cdot 5$

Multiply $3$ by $5$ .

$4 x^{2} + 6 x y + 10 x + 6 y x + 9 y^{2} + 15 y + 10 x + 15 y + 5 \cdot 5$

Multiply $5$ by $5$ .

$4 x^{2} + 6 x y + 10 x + 6 y x + 9 y^{2} + 15 y + 10 x + 15 y + 25$

Add $6 x y$ and $6 y x$ .

Move $y$ .

$4 x^{2} + 6 x y + 6 x y + 10 x + 9 y^{2} + 15 y + 10 x + 15 y + 25$

Add $6 x y$ and $6 x y$ .

$4 x^{2} + 12 x y + 10 x + 9 y^{2} + 15 y + 10 x + 15 y + 25$

Add $10 x$ and $10 x$ .

$4 x^{2} + 12 x y + 20 x + 9 y^{2} + 15 y + 15 y + 25$

Add $15 y$ and $15 y$ .

$4 x^{2} + 12 x y + 20 x + 9 y^{2} + 30 y + 25$

Find the Product (2x+3y+5)^2

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