Simplify (2s^2p-5w^2)^2

${(2 s^{2} p - 5 w^{2})}^{2}$

Step 1

Rewrite ${(2 s^{2} p - 5 w^{2})}^{2}$ as $(2 s^{2} p - 5 w^{2}) (2 s^{2} p - 5 w^{2})$ .

$(2 s^{2} p - 5 w^{2}) (2 s^{2} p - 5 w^{2})$

Step 2

Expand $(2 s^{2} p - 5 w^{2}) (2 s^{2} p - 5 w^{2})$ using the FOIL Method.

Apply the distributive property.

$2 s^{2} p (2 s^{2} p - 5 w^{2}) - 5 w^{2} (2 s^{2} p - 5 w^{2})$

Apply the distributive property.

$2 s^{2} p (2 s^{2} p) + 2 s^{2} p (- 5 w^{2}) - 5 w^{2} (2 s^{2} p - 5 w^{2})$

Apply the distributive property.

$2 s^{2} p (2 s^{2} p) + 2 s^{2} p (- 5 w^{2}) - 5 w^{2} (2 s^{2} p) - 5 w^{2} (- 5 w^{2})$

Step 3

Simplify and combine like terms.

Simplify each term.

Multiply $s^{2}$ by $s^{2}$ by adding the exponents.

Move $s^{2}$ .

$2 (s^{2} s^{2}) p (2 p) + 2 s^{2} p (- 5 w^{2}) - 5 w^{2} (2 s^{2} p) - 5 w^{2} (- 5 w^{2})$

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$2 s^{2 + 2} p (2 p) + 2 s^{2} p (- 5 w^{2}) - 5 w^{2} (2 s^{2} p) - 5 w^{2} (- 5 w^{2})$

Add $2$ and $2$ .

$2 s^{4} p (2 p) + 2 s^{2} p (- 5 w^{2}) - 5 w^{2} (2 s^{2} p) - 5 w^{2} (- 5 w^{2})$

Multiply $p$ by $p$ by adding the exponents.

Move $p$ .

$2 s^{4} (p \cdot p) \cdot 2 + 2 s^{2} p (- 5 w^{2}) - 5 w^{2} (2 s^{2} p) - 5 w^{2} (- 5 w^{2})$

Multiply $p$ by $p$ .

$2 s^{4} p^{2} \cdot 2 + 2 s^{2} p (- 5 w^{2}) - 5 w^{2} (2 s^{2} p) - 5 w^{2} (- 5 w^{2})$

Multiply $2$ by $2$ .

$4 s^{4} p^{2} + 2 s^{2} p (- 5 w^{2}) - 5 w^{2} (2 s^{2} p) - 5 w^{2} (- 5 w^{2})$

Multiply $- 5$ by $2$ .

$4 s^{4} p^{2} - 10 s^{2} p w^{2} - 5 w^{2} (2 s^{2} p) - 5 w^{2} (- 5 w^{2})$

Multiply $2$ by $- 5$ .

$4 s^{4} p^{2} - 10 s^{2} p w^{2} - 10 w^{2} (s^{2} p) - 5 w^{2} (- 5 w^{2})$

Rewrite using the commutative property of multiplication.

$4 s^{4} p^{2} - 10 s^{2} p w^{2} - 10 w^{2} s^{2} p - 5 \cdot - 5 w^{2} w^{2}$

Multiply $w^{2}$ by $w^{2}$ by adding the exponents.

Move $w^{2}$ .

$4 s^{4} p^{2} - 10 s^{2} p w^{2} - 10 w^{2} s^{2} p - 5 \cdot - 5 (w^{2} w^{2})$

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$4 s^{4} p^{2} - 10 s^{2} p w^{2} - 10 w^{2} s^{2} p - 5 \cdot - 5 w^{2 + 2}$

Add $2$ and $2$ .

$4 s^{4} p^{2} - 10 s^{2} p w^{2} - 10 w^{2} s^{2} p - 5 \cdot - 5 w^{4}$

Multiply $- 5$ by $- 5$ .

$4 s^{4} p^{2} - 10 s^{2} p w^{2} - 10 w^{2} s^{2} p + 25 w^{4}$

Move $s^{2}$ .

$4 s^{4} p^{2} - 10 p s^{2} w^{2} - 10 p s^{2} w^{2} + 25 w^{4}$

Subtract $10 p s^{2} w^{2}$ from $- 10 p s^{2} w^{2}$ .

$4 s^{4} p^{2} - 20 p s^{2} w^{2} + 25 w^{4}$

Step 4

Move $s^{4}$ .

$4 p^{2} s^{4} - 20 p s^{2} w^{2} + 25 w^{4}$

Simplify (2s^2p-5w^2)^2

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