Write in Standard Form (2r+3)^2+(r+4)^2=10

${(2 r + 3)}^{2} + {(r + 4)}^{2} = 10$

Subtract $10$ from both sides of the equation.

${(2 r + 3)}^{2} + {(r + 4)}^{2} - 10 = 0$

Simplify ${(2 r + 3)}^{2} + {(r + 4)}^{2} - 10$ .

Simplify each term.

Rewrite ${(2 r + 3)}^{2}$ as $(2 r + 3) (2 r + 3)$ .

$(2 r + 3) (2 r + 3) + {(r + 4)}^{2} - 10 = 0$

Expand $(2 r + 3) (2 r + 3)$ using the FOIL Method.

Apply the distributive property.

$2 r (2 r + 3) + 3 (2 r + 3) + {(r + 4)}^{2} - 10 = 0$

Apply the distributive property.

$2 r (2 r) + 2 r \cdot 3 + 3 (2 r + 3) + {(r + 4)}^{2} - 10 = 0$

Apply the distributive property.

$2 r (2 r) + 2 r \cdot 3 + 3 (2 r) + 3 \cdot 3 + {(r + 4)}^{2} - 10 = 0$

Simplify and combine like terms.

Simplify each term.

Rewrite using the commutative property of multiplication.

$2 \cdot 2 r \cdot r + 2 r \cdot 3 + 3 (2 r) + 3 \cdot 3 + {(r + 4)}^{2} - 10 = 0$

Multiply $r$ by $r$ by adding the exponents.

Move $r$ .

$2 \cdot 2 (r \cdot r) + 2 r \cdot 3 + 3 (2 r) + 3 \cdot 3 + {(r + 4)}^{2} - 10 = 0$

Multiply $r$ by $r$ .

$2 \cdot 2 r^{2} + 2 r \cdot 3 + 3 (2 r) + 3 \cdot 3 + {(r + 4)}^{2} - 10 = 0$

Multiply $2$ by $2$ .

$4 r^{2} + 2 r \cdot 3 + 3 (2 r) + 3 \cdot 3 + {(r + 4)}^{2} - 10 = 0$

Multiply $3$ by $2$ .

$4 r^{2} + 6 r + 3 (2 r) + 3 \cdot 3 + {(r + 4)}^{2} - 10 = 0$

Multiply $2$ by $3$ .

$4 r^{2} + 6 r + 6 r + 3 \cdot 3 + {(r + 4)}^{2} - 10 = 0$

Multiply $3$ by $3$ .

$4 r^{2} + 6 r + 6 r + 9 + {(r + 4)}^{2} - 10 = 0$

Add $6 r$ and $6 r$ .

$4 r^{2} + 12 r + 9 + {(r + 4)}^{2} - 10 = 0$

Rewrite ${(r + 4)}^{2}$ as $(r + 4) (r + 4)$ .

$4 r^{2} + 12 r + 9 + (r + 4) (r + 4) - 10 = 0$

Expand $(r + 4) (r + 4)$ using the FOIL Method.

Apply the distributive property.

$4 r^{2} + 12 r + 9 + r (r + 4) + 4 (r + 4) - 10 = 0$

Apply the distributive property.

$4 r^{2} + 12 r + 9 + r \cdot r + r \cdot 4 + 4 (r + 4) - 10 = 0$

Apply the distributive property.

$4 r^{2} + 12 r + 9 + r \cdot r + r \cdot 4 + 4 r + 4 \cdot 4 - 10 = 0$

Simplify and combine like terms.

Simplify each term.

Multiply $r$ by $r$ .

$4 r^{2} + 12 r + 9 + r^{2} + r \cdot 4 + 4 r + 4 \cdot 4 - 10 = 0$

Move $4$ to the left of $r$ .

$4 r^{2} + 12 r + 9 + r^{2} + 4 \cdot r + 4 r + 4 \cdot 4 - 10 = 0$

Multiply $4$ by $4$ .

$4 r^{2} + 12 r + 9 + r^{2} + 4 r + 4 r + 16 - 10 = 0$

Add $4 r$ and $4 r$ .

$4 r^{2} + 12 r + 9 + r^{2} + 8 r + 16 - 10 = 0$

Add $4 r^{2}$ and $r^{2}$ .

$5 r^{2} + 12 r + 9 + 8 r + 16 - 10 = 0$

Add $12 r$ and $8 r$ .

$5 r^{2} + 20 r + 9 + 16 - 10 = 0$

Add $9$ and $16$ .

$5 r^{2} + 20 r + 25 - 10 = 0$

Subtract $10$ from $25$ .

$5 r^{2} + 20 r + 15 = 0$

To write a polynomial in standard form, simplify and then arrange the terms in descending order.

$a x^{2} + b x + c = 0$

The standard form is $5 r^{2} + 20 r + 15$ .

$5 r^{2} + 20 r + 15 = 0$

Write in Standard Form (2r+3)^2+(r+4)^2=10

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