Question

Simplify: (p+q)(p2-q2)+(p-q)(p2+q2)​

Answer 1

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)

•••♪

Answer 2

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)