Find the Expanded Form (2x+0.09)^2+(2y-6)^2=4

${(2 x + 0.09)}^{2} + {(2 y - 6)}^{2} = 4$

Step 1

Simplify the left side ${(2 x + 0.09)}^{2} + {(2 y - 6)}^{2}$ .

Simplify each term.

Rewrite ${(2 x + 0.09)}^{2}$ as $(2 x + 0.09) (2 x + 0.09)$ .

$(2 x + 0.09) (2 x + 0.09) + {(2 y - 6)}^{2} = 4$

Expand $(2 x + 0.09) (2 x + 0.09)$ using the FOIL Method.

Apply the distributive property.

$2 x (2 x + 0.09) + 0.09 (2 x + 0.09) + {(2 y - 6)}^{2} = 4$

Apply the distributive property.

$2 x (2 x) + 2 x \cdot 0.09 + 0.09 (2 x + 0.09) + {(2 y - 6)}^{2} = 4$

Apply the distributive property.

$2 x (2 x) + 2 x \cdot 0.09 + 0.09 (2 x) + 0.09 \cdot 0.09 + {(2 y - 6)}^{2} = 4$

Simplify and combine like terms.

Simplify each term.

Rewrite using the commutative property of multiplication.

$2 \cdot (2 x \cdot x) + 2 x \cdot 0.09 + 0.09 (2 x) + 0.09 \cdot 0.09 + {(2 y - 6)}^{2} = 4$

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

Move $x$ .

$2 \cdot (2 (x \cdot x)) + 2 x \cdot 0.09 + 0.09 (2 x) + 0.09 \cdot 0.09 + {(2 y - 6)}^{2} = 4$

Multiply $x$ by $x$ .

$2 \cdot (2 x^{2}) + 2 x \cdot 0.09 + 0.09 (2 x) + 0.09 \cdot 0.09 + {(2 y - 6)}^{2} = 4$

Multiply $2$ by $2$ .

$4 x^{2} + 2 x \cdot 0.09 + 0.09 (2 x) + 0.09 \cdot 0.09 + {(2 y - 6)}^{2} = 4$

Multiply $0.09$ by $2$ .

$4 x^{2} + 0.18 x + 0.09 (2 x) + 0.09 \cdot 0.09 + {(2 y - 6)}^{2} = 4$

Multiply $2$ by $0.09$ .

$4 x^{2} + 0.18 x + 0.18 x + 0.09 \cdot 0.09 + {(2 y - 6)}^{2} = 4$

Multiply $0.09$ by $0.09$ .

$4 x^{2} + 0.18 x + 0.18 x + 0.0081 + {(2 y - 6)}^{2} = 4$

Add $0.18 x$ and $0.18 x$ .

$4 x^{2} + 0.36 x + 0.0081 + {(2 y - 6)}^{2} = 4$

Rewrite ${(2 y - 6)}^{2}$ as $(2 y - 6) (2 y - 6)$ .

$4 x^{2} + 0.36 x + 0.0081 + (2 y - 6) (2 y - 6) = 4$

Expand $(2 y - 6) (2 y - 6)$ using the FOIL Method.

Apply the distributive property.

$4 x^{2} + 0.36 x + 0.0081 + 2 y (2 y - 6) - 6 (2 y - 6) = 4$

Apply the distributive property.

$4 x^{2} + 0.36 x + 0.0081 + 2 y (2 y) + 2 y \cdot - 6 - 6 (2 y - 6) = 4$

Apply the distributive property.

$4 x^{2} + 0.36 x + 0.0081 + 2 y (2 y) + 2 y \cdot - 6 - 6 (2 y) - 6 \cdot - 6 = 4$

Simplify and combine like terms.

Simplify each term.

Rewrite using the commutative property of multiplication.

$4 x^{2} + 0.36 x + 0.0081 + 2 \cdot (2 y \cdot y) + 2 y \cdot - 6 - 6 (2 y) - 6 \cdot - 6 = 4$

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

Move $y$ .

$4 x^{2} + 0.36 x + 0.0081 + 2 \cdot (2 (y \cdot y)) + 2 y \cdot - 6 - 6 (2 y) - 6 \cdot - 6 = 4$

Multiply $y$ by $y$ .

$4 x^{2} + 0.36 x + 0.0081 + 2 \cdot (2 y^{2}) + 2 y \cdot - 6 - 6 (2 y) - 6 \cdot - 6 = 4$

Multiply $2$ by $2$ .

$4 x^{2} + 0.36 x + 0.0081 + 4 y^{2} + 2 y \cdot - 6 - 6 (2 y) - 6 \cdot - 6 = 4$

Multiply $- 6$ by $2$ .

$4 x^{2} + 0.36 x + 0.0081 + 4 y^{2} - 12 y - 6 (2 y) - 6 \cdot - 6 = 4$

Multiply $2$ by $- 6$ .

$4 x^{2} + 0.36 x + 0.0081 + 4 y^{2} - 12 y - 12 y - 6 \cdot - 6 = 4$

Multiply $- 6$ by $- 6$ .

$4 x^{2} + 0.36 x + 0.0081 + 4 y^{2} - 12 y - 12 y + 36 = 4$

Subtract $12 y$ from $- 12 y$ .

$4 x^{2} + 0.36 x + 0.0081 + 4 y^{2} - 24 y + 36 = 4$

Simplify the expression.

Add $0.0081$ and $36$ .

$4 x^{2} + 0.36 x + 4 y^{2} - 24 y + 36.0081 = 4$

Move $0.36 x$ .

$4 x^{2} + 4 y^{2} + 0.36 x - 24 y + 36.0081 = 4$

Step 2

Subtract $4$ from both sides of the equation.

$4 x^{2} + 4 y^{2} + 0.36 x - 24 y + 36.0081 - 4 = 0$

Step 3

Subtract $4$ from $36.0081$ .

$4 x^{2} + 4 y^{2} + 0.36 x - 24 y + 32.0081 = 0$

Find the Expanded Form (2x+0.09)^2+(2y-6)^2=4

Related Questions

Support LCMGCF.com by disabling your adblocker.