Simplify (2p^2+7q)(2p^2-7q)

$(2 p^{2} + 7 q) (2 p^{2} - 7 q)$

Step 1

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

Apply the distributive property.

$2 p^{2} (2 p^{2} - 7 q) + 7 q (2 p^{2} - 7 q)$

Apply the distributive property.

$2 p^{2} (2 p^{2}) + 2 p^{2} (- 7 q) + 7 q (2 p^{2} - 7 q)$

Apply the distributive property.

$2 p^{2} (2 p^{2}) + 2 p^{2} (- 7 q) + 7 q (2 p^{2}) + 7 q (- 7 q)$

Step 2

Simplify and combine like terms.

Simplify each term.

Rewrite using the commutative property of multiplication.

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

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

Move $p^{2}$ .

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

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

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

Add $2$ and $2$ .

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

Multiply $2$ by $2$ .

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

Rewrite using the commutative property of multiplication.

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

Multiply $2$ by $- 7$ .

$4 p^{4} - 14 p^{2} q + 7 q (2 p^{2}) + 7 q (- 7 q)$

Rewrite using the commutative property of multiplication.

$4 p^{4} - 14 p^{2} q + 7 \cdot 2 q p^{2} + 7 q (- 7 q)$

Multiply $7$ by $2$ .

$4 p^{4} - 14 p^{2} q + 14 q p^{2} + 7 q (- 7 q)$

Rewrite using the commutative property of multiplication.

$4 p^{4} - 14 p^{2} q + 14 q p^{2} + 7 \cdot - 7 q \cdot q$

Multiply $q$ by $q$ by adding the exponents.

Move $q$ .

$4 p^{4} - 14 p^{2} q + 14 q p^{2} + 7 \cdot - 7 (q \cdot q)$

Multiply $q$ by $q$ .

$4 p^{4} - 14 p^{2} q + 14 q p^{2} + 7 \cdot - 7 q^{2}$

Multiply $7$ by $- 7$ .

$4 p^{4} - 14 p^{2} q + 14 q p^{2} - 49 q^{2}$

Add $- 14 p^{2} q$ and $14 q p^{2}$ .

Move $q$ .

$4 p^{4} - 14 p^{2} q + 14 p^{2} q - 49 q^{2}$

Add $- 14 p^{2} q$ and $14 p^{2} q$ .

$4 p^{4} + 0 - 49 q^{2}$

Add $4 p^{4}$ and $0$ .

$4 p^{4} - 49 q^{2}$

Simplify (2p^2+7q)(2p^2-7q)

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