Simplify 2(1+5m)^2+18(1+5m)-14

$2 {(1 + 5 m)}^{2} + 18 (1 + 5 m) - 14$

Simplify each term.

Rewrite ${(1 + 5 m)}^{2}$ as $(1 + 5 m) (1 + 5 m)$ .

$2 ((1 + 5 m) (1 + 5 m)) + 18 (1 + 5 m) - 14$

Expand $(1 + 5 m) (1 + 5 m)$ using the FOIL Method.

Apply the distributive property.

$2 (1 (1 + 5 m) + 5 m (1 + 5 m)) + 18 (1 + 5 m) - 14$

Apply the distributive property.

$2 (1 \cdot 1 + 1 (5 m) + 5 m (1 + 5 m)) + 18 (1 + 5 m) - 14$

Apply the distributive property.

$2 (1 \cdot 1 + 1 (5 m) + 5 m \cdot 1 + 5 m (5 m)) + 18 (1 + 5 m) - 14$

Simplify and combine like terms.

Simplify each term.

Multiply $1$ by $1$ .

$2 (1 + 1 (5 m) + 5 m \cdot 1 + 5 m (5 m)) + 18 (1 + 5 m) - 14$

Multiply $5 m$ by $1$ .

$2 (1 + 5 m + 5 m \cdot 1 + 5 m (5 m)) + 18 (1 + 5 m) - 14$

Multiply $5$ by $1$ .

$2 (1 + 5 m + 5 m + 5 m (5 m)) + 18 (1 + 5 m) - 14$

Rewrite using the commutative property of multiplication.

$2 (1 + 5 m + 5 m + 5 \cdot 5 m \cdot m) + 18 (1 + 5 m) - 14$

Multiply $m$ by $m$ by adding the exponents.

Move $m$ .

$2 (1 + 5 m + 5 m + 5 \cdot 5 (m \cdot m)) + 18 (1 + 5 m) - 14$

Multiply $m$ by $m$ .

$2 (1 + 5 m + 5 m + 5 \cdot 5 m^{2}) + 18 (1 + 5 m) - 14$

Multiply $5$ by $5$ .

$2 (1 + 5 m + 5 m + 25 m^{2}) + 18 (1 + 5 m) - 14$

Add $5 m$ and $5 m$ .

$2 (1 + 10 m + 25 m^{2}) + 18 (1 + 5 m) - 14$

Apply the distributive property.

$2 \cdot 1 + 2 (10 m) + 2 (25 m^{2}) + 18 (1 + 5 m) - 14$

Simplify.

Multiply $2$ by $1$ .

$2 + 2 (10 m) + 2 (25 m^{2}) + 18 (1 + 5 m) - 14$

Multiply $10$ by $2$ .

$2 + 20 m + 2 (25 m^{2}) + 18 (1 + 5 m) - 14$

Multiply $25$ by $2$ .

$2 + 20 m + 50 m^{2} + 18 (1 + 5 m) - 14$

Apply the distributive property.

$2 + 20 m + 50 m^{2} + 18 \cdot 1 + 18 (5 m) - 14$

Multiply $18$ by $1$ .

$2 + 20 m + 50 m^{2} + 18 + 18 (5 m) - 14$

Multiply $5$ by $18$ .

$2 + 20 m + 50 m^{2} + 18 + 90 m - 14$

Simplify by adding terms.

Add $2$ and $18$ .

$20 m + 50 m^{2} + 20 + 90 m - 14$

Add $20 m$ and $90 m$ .

$110 m + 50 m^{2} + 20 - 14$

Simplify the expression.

Subtract $14$ from $20$ .

$110 m + 50 m^{2} + 6$

Reorder $110 m$ and $50 m^{2}$ .

$50 m^{2} + 110 m + 6$

Simplify 2(1+5m)^2+18(1+5m)-14

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