- p
^{4}+ 2p^{2}q^{2}- 4p^{3}q - p4 - 2p2q2 - 4p3
- p4 + 2p2q2 + 4p3
- p4 - 2p2q2 + 4p3

Option 1 : p^{4} + 2p^{2}q^{2} - 4p^{3}q

**Given**

a + b = p

ab = pq

**Formula Used**

(a + b)^{2} = a^{2 }+ b^{2} + 2ab

**Calculation Used**

a + b = p

Squaring both side

⇒ (a + b)2 = p^{2}

⇒ a2 + b2 + 2ab = p^{2}

⇒ a2 + b2 = p^{2} - 2pq

Squaring again both side

(a2 + b2)^{2 }= (p2 - 2pq)^{2}

⇒ a4 + b^{4} + 2a^{2}b^{2} = p^{4} + 4p^{2}q^{2} - 4p^{3}q

⇒ a4 + b4 = p4 + 2p2q2 - 4p3q

**∴ The required answer is p4 + 2p2q2 - 4p3q**

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