Simplify (3x-5)^2+(5x+2)^2

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

Simplify each term.

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

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

Expand $(3 x - 5) (3 x - 5)$ using the FOIL Method.

Apply the distributive property.

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

Apply the distributive property.

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

Apply the distributive property.

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

Simplify and combine like terms.

Simplify each term.

Rewrite using the commutative property of multiplication.

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

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

Move $x$ .

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

Multiply $x$ by $x$ .

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

Multiply $3$ by $3$ .

$9 x^{2} + 3 x \cdot - 5 - 5 (3 x) - 5 \cdot - 5 + {(5 x + 2)}^{2}$

Multiply $- 5$ by $3$ .

$9 x^{2} - 15 x - 5 (3 x) - 5 \cdot - 5 + {(5 x + 2)}^{2}$

Multiply $3$ by $- 5$ .

$9 x^{2} - 15 x - 15 x - 5 \cdot - 5 + {(5 x + 2)}^{2}$

Multiply $- 5$ by $- 5$ .

$9 x^{2} - 15 x - 15 x + 25 + {(5 x + 2)}^{2}$

Subtract $15 x$ from $- 15 x$ .

$9 x^{2} - 30 x + 25 + {(5 x + 2)}^{2}$

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

$9 x^{2} - 30 x + 25 + (5 x + 2) (5 x + 2)$

Expand $(5 x + 2) (5 x + 2)$ using the FOIL Method.

Apply the distributive property.

$9 x^{2} - 30 x + 25 + 5 x (5 x + 2) + 2 (5 x + 2)$

Apply the distributive property.

$9 x^{2} - 30 x + 25 + 5 x (5 x) + 5 x \cdot 2 + 2 (5 x + 2)$

Apply the distributive property.

$9 x^{2} - 30 x + 25 + 5 x (5 x) + 5 x \cdot 2 + 2 (5 x) + 2 \cdot 2$

Simplify and combine like terms.

Simplify each term.

Rewrite using the commutative property of multiplication.

$9 x^{2} - 30 x + 25 + 5 \cdot 5 x \cdot x + 5 x \cdot 2 + 2 (5 x) + 2 \cdot 2$

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

Move $x$ .

$9 x^{2} - 30 x + 25 + 5 \cdot 5 (x \cdot x) + 5 x \cdot 2 + 2 (5 x) + 2 \cdot 2$

Multiply $x$ by $x$ .

$9 x^{2} - 30 x + 25 + 5 \cdot 5 x^{2} + 5 x \cdot 2 + 2 (5 x) + 2 \cdot 2$

Multiply $5$ by $5$ .

$9 x^{2} - 30 x + 25 + 25 x^{2} + 5 x \cdot 2 + 2 (5 x) + 2 \cdot 2$

Multiply $2$ by $5$ .

$9 x^{2} - 30 x + 25 + 25 x^{2} + 10 x + 2 (5 x) + 2 \cdot 2$

Multiply $5$ by $2$ .

$9 x^{2} - 30 x + 25 + 25 x^{2} + 10 x + 10 x + 2 \cdot 2$

Multiply $2$ by $2$ .

$9 x^{2} - 30 x + 25 + 25 x^{2} + 10 x + 10 x + 4$

Add $10 x$ and $10 x$ .

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

Simplify by adding terms.

Add $9 x^{2}$ and $25 x^{2}$ .

$34 x^{2} - 30 x + 25 + 20 x + 4$

Add $- 30 x$ and $20 x$ .

$34 x^{2} - 10 x + 25 + 4$

Add $25$ and $4$ .

$34 x^{2} - 10 x + 29$

Simplify (3x-5)^2+(5x+2)^2

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