Find the Perfect Square Trinomial (-2m+5n)^2

${(- 2 m + 5 n)}^{2}$

Step 1

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

$(- 2 m + 5 n) (- 2 m + 5 n)$

Step 2

Expand $(- 2 m + 5 n) (- 2 m + 5 n)$ using the FOIL Method.

Apply the distributive property.

$- 2 m (- 2 m + 5 n) + 5 n (- 2 m + 5 n)$

Apply the distributive property.

$- 2 m (- 2 m) - 2 m (5 n) + 5 n (- 2 m + 5 n)$

Apply the distributive property.

$- 2 m (- 2 m) - 2 m (5 n) + 5 n (- 2 m) + 5 n (5 n)$

Step 3

Simplify and combine like terms.

Simplify each term.

Rewrite using the commutative property of multiplication.

$- 2 \cdot - 2 m \cdot m - 2 m (5 n) + 5 n (- 2 m) + 5 n (5 n)$

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

Move $m$ .

$- 2 \cdot - 2 (m \cdot m) - 2 m (5 n) + 5 n (- 2 m) + 5 n (5 n)$

Multiply $m$ by $m$ .

$- 2 \cdot - 2 m^{2} - 2 m (5 n) + 5 n (- 2 m) + 5 n (5 n)$

Multiply $- 2$ by $- 2$ .

$4 m^{2} - 2 m (5 n) + 5 n (- 2 m) + 5 n (5 n)$

Rewrite using the commutative property of multiplication.

$4 m^{2} - 2 \cdot 5 m n + 5 n (- 2 m) + 5 n (5 n)$

Multiply $- 2$ by $5$ .

$4 m^{2} - 10 m n + 5 n (- 2 m) + 5 n (5 n)$

Rewrite using the commutative property of multiplication.

$4 m^{2} - 10 m n + 5 \cdot - 2 n m + 5 n (5 n)$

Multiply $5$ by $- 2$ .

$4 m^{2} - 10 m n - 10 n m + 5 n (5 n)$

Rewrite using the commutative property of multiplication.

$4 m^{2} - 10 m n - 10 n m + 5 \cdot 5 n \cdot n$

Multiply $n$ by $n$ by adding the exponents.

Move $n$ .

$4 m^{2} - 10 m n - 10 n m + 5 \cdot 5 (n \cdot n)$

Multiply $n$ by $n$ .

$4 m^{2} - 10 m n - 10 n m + 5 \cdot 5 n^{2}$

Multiply $5$ by $5$ .

$4 m^{2} - 10 m n - 10 n m + 25 n^{2}$

Subtract $10 n m$ from $- 10 m n$ .

Move $n$ .

$4 m^{2} - 10 m n - 10 m n + 25 n^{2}$

Subtract $10 m n$ from $- 10 m n$ .

$4 m^{2} - 20 m n + 25 n^{2}$

Find the Perfect Square Trinomial (-2m+5n)^2

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