simplify:
(P+Q) (P-Q) (P²+PQ+Q²) (P²-PQ×Q²)
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Answer:
2(p³-q³)
Step-by-step explanation:
(p+q)(p²-q²)+(p-q)(p²+q²)
= (p+q)(p+q)(p-q)+(p-q)(p²+q²)
/* By algebraic identity:
x²-y² = (x+y)(x-y) */
= (p-q)[(p+q)²+(p²+q²)]
= (p-q)[p²+2pq+q²+p²+q²]
= (p-q)(2p²+2pq+2q²)
= 2(p-q)(p²+pq+q²)
= 2(p³-q³)
/* By algebraic identity:
(x-y)(x²+xy+y²) = x³-y³ */
Therefore,
(p+q)(p²-q²)+(p-q)(p²+q²)
= 2(p³-q³)
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