Find the Expanded Form (x+5)^2-y^2=125

${(x + 5)}^{2} - y^{2} = 125$

Step 1

Simplify the left side ${(x + 5)}^{2} - y^{2}$ .

Simplify each term.

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

$(x + 5) (x + 5) - y^{2} = 125$

Expand $(x + 5) (x + 5)$ using the FOIL Method.

Apply the distributive property.

$x (x + 5) + 5 (x + 5) - y^{2} = 125$

Apply the distributive property.

$x \cdot x + x \cdot 5 + 5 (x + 5) - y^{2} = 125$

Apply the distributive property.

$x \cdot x + x \cdot 5 + 5 x + 5 \cdot 5 - y^{2} = 125$

Simplify and combine like terms.

Simplify each term.

Multiply $x$ by $x$ .

$x^{2} + x \cdot 5 + 5 x + 5 \cdot 5 - y^{2} = 125$

Move $5$ to the left of $x$ .

$x^{2} + 5 \cdot x + 5 x + 5 \cdot 5 - y^{2} = 125$

Multiply $5$ by $5$ .

$x^{2} + 5 x + 5 x + 25 - y^{2} = 125$

Add $5 x$ and $5 x$ .

$x^{2} + 10 x + 25 - y^{2} = 125$

Reorder.

Move $25$ .

$x^{2} + 10 x - y^{2} + 25 = 125$

Move $10 x$ .

$x^{2} - y^{2} + 10 x + 25 = 125$

Step 2

Set the equation equal to zero.

Subtract $125$ from both sides of the equation.

$x^{2} - y^{2} + 10 x + 25 - 125 = 0$

Subtract $125$ from $25$ .

$x^{2} - y^{2} + 10 x - 100 = 0$