Find the Perfect Square Trinomial (7q^2w^2-4w^2)^2

${(7 q^{2} w^{2} - 4 w^{2})}^{2}$

Step 1

Rewrite ${(7 q^{2} w^{2} - 4 w^{2})}^{2}$ as $(7 q^{2} w^{2} - 4 w^{2}) (7 q^{2} w^{2} - 4 w^{2})$ .

$(7 q^{2} w^{2} - 4 w^{2}) (7 q^{2} w^{2} - 4 w^{2})$

Step 2

Expand $(7 q^{2} w^{2} - 4 w^{2}) (7 q^{2} w^{2} - 4 w^{2})$ using the FOIL Method.

Apply the distributive property.

$7 q^{2} w^{2} (7 q^{2} w^{2} - 4 w^{2}) - 4 w^{2} (7 q^{2} w^{2} - 4 w^{2})$

Apply the distributive property.

$7 q^{2} w^{2} (7 q^{2} w^{2}) + 7 q^{2} w^{2} (- 4 w^{2}) - 4 w^{2} (7 q^{2} w^{2} - 4 w^{2})$

Apply the distributive property.

$7 q^{2} w^{2} (7 q^{2} w^{2}) + 7 q^{2} w^{2} (- 4 w^{2}) - 4 w^{2} (7 q^{2} w^{2}) - 4 w^{2} (- 4 w^{2})$

Step 3

Simplify and combine like terms.

Simplify each term.

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

Move $q^{2}$ .

$7 (q^{2} q^{2}) w^{2} (7 w^{2}) + 7 q^{2} w^{2} (- 4 w^{2}) - 4 w^{2} (7 q^{2} w^{2}) - 4 w^{2} (- 4 w^{2})$

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

$7 q^{2 + 2} w^{2} (7 w^{2}) + 7 q^{2} w^{2} (- 4 w^{2}) - 4 w^{2} (7 q^{2} w^{2}) - 4 w^{2} (- 4 w^{2})$

Add $2$ and $2$ .

$7 q^{4} w^{2} (7 w^{2}) + 7 q^{2} w^{2} (- 4 w^{2}) - 4 w^{2} (7 q^{2} w^{2}) - 4 w^{2} (- 4 w^{2})$

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

Move $w^{2}$ .

$7 q^{4} (w^{2} w^{2}) \cdot 7 + 7 q^{2} w^{2} (- 4 w^{2}) - 4 w^{2} (7 q^{2} w^{2}) - 4 w^{2} (- 4 w^{2})$

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

$7 q^{4} w^{2 + 2} \cdot 7 + 7 q^{2} w^{2} (- 4 w^{2}) - 4 w^{2} (7 q^{2} w^{2}) - 4 w^{2} (- 4 w^{2})$

Add $2$ and $2$ .

$7 q^{4} w^{4} \cdot 7 + 7 q^{2} w^{2} (- 4 w^{2}) - 4 w^{2} (7 q^{2} w^{2}) - 4 w^{2} (- 4 w^{2})$

Multiply $7$ by $7$ .

$49 q^{4} w^{4} + 7 q^{2} w^{2} (- 4 w^{2}) - 4 w^{2} (7 q^{2} w^{2}) - 4 w^{2} (- 4 w^{2})$

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

Move $w^{2}$ .

$49 q^{4} w^{4} + 7 q^{2} (w^{2} w^{2}) \cdot - 4 - 4 w^{2} (7 q^{2} w^{2}) - 4 w^{2} (- 4 w^{2})$

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

$49 q^{4} w^{4} + 7 q^{2} w^{2 + 2} \cdot - 4 - 4 w^{2} (7 q^{2} w^{2}) - 4 w^{2} (- 4 w^{2})$

Add $2$ and $2$ .

$49 q^{4} w^{4} + 7 q^{2} w^{4} \cdot - 4 - 4 w^{2} (7 q^{2} w^{2}) - 4 w^{2} (- 4 w^{2})$

Multiply $- 4$ by $7$ .

$49 q^{4} w^{4} - 28 q^{2} w^{4} - 4 w^{2} (7 q^{2} w^{2}) - 4 w^{2} (- 4 w^{2})$

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

Move $w^{2}$ .

$49 q^{4} w^{4} - 28 q^{2} w^{4} - 4 (w^{2} w^{2}) (7 q^{2}) - 4 w^{2} (- 4 w^{2})$

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

$49 q^{4} w^{4} - 28 q^{2} w^{4} - 4 w^{2 + 2} (7 q^{2}) - 4 w^{2} (- 4 w^{2})$

Add $2$ and $2$ .

$49 q^{4} w^{4} - 28 q^{2} w^{4} - 4 w^{4} (7 q^{2}) - 4 w^{2} (- 4 w^{2})$

Rewrite using the commutative property of multiplication.

$49 q^{4} w^{4} - 28 q^{2} w^{4} - 4 \cdot 7 w^{4} q^{2} - 4 w^{2} (- 4 w^{2})$

Multiply $- 4$ by $7$ .

$49 q^{4} w^{4} - 28 q^{2} w^{4} - 28 w^{4} q^{2} - 4 w^{2} (- 4 w^{2})$

Rewrite using the commutative property of multiplication.

$49 q^{4} w^{4} - 28 q^{2} w^{4} - 28 w^{4} q^{2} - 4 \cdot - 4 w^{2} w^{2}$

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

Move $w^{2}$ .

$49 q^{4} w^{4} - 28 q^{2} w^{4} - 28 w^{4} q^{2} - 4 \cdot - 4 (w^{2} w^{2})$

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

$49 q^{4} w^{4} - 28 q^{2} w^{4} - 28 w^{4} q^{2} - 4 \cdot - 4 w^{2 + 2}$

Add $2$ and $2$ .

$49 q^{4} w^{4} - 28 q^{2} w^{4} - 28 w^{4} q^{2} - 4 \cdot - 4 w^{4}$

Multiply $- 4$ by $- 4$ .

$49 q^{4} w^{4} - 28 q^{2} w^{4} - 28 w^{4} q^{2} + 16 w^{4}$

Subtract $28 w^{4} q^{2}$ from $- 28 q^{2} w^{4}$ .

Move $w^{4}$ .

$49 q^{4} w^{4} - 28 q^{2} w^{4} - 28 q^{2} w^{4} + 16 w^{4}$

Subtract $28 q^{2} w^{4}$ from $- 28 q^{2} w^{4}$ .

$49 q^{4} w^{4} - 56 q^{2} w^{4} + 16 w^{4}$

Find the Perfect Square Trinomial (7q^2w^2-4w^2)^2

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