Q. 125.0( 6 Votes )

Let’s find the pr

Answer :

Formula used:


(a + b)(a – b) = a2 – b2


i. (xy + pq)(xy – pq)


Taking a = xy and b = pq, then from above identity,


= (xy)2 – (pq)2


= x2y2 – p2q2


ii. 49 × 51


= (50 – 1)(50 + 1)


Taking a = 50 and b = 1, then from above identity,


= 502 - 12


= 2500 – 1


= 2499


iii. (2x – y + 3z)(2x + y + 3z)


Taking a = 2x and b = y + 3z, the from the above identity we have


= (2x)2 – (y + 3z)2


= 4x2 – (y2 + 2(y)(3z) + (3z)2) [ (a + b)2 = a2 + 2ab + b2]


= 4x2 – (y2 + 6yz + 9z2)


= 4x2 – y2 – 6yz – 9z2


iv. 1511 × 1489


= (1500 + 11)(1500 – 11)


Taking a = 1500 and b = 11, then from above identity,


= (1500)2 - 112


= 2250000 – 121


= 2249879


v. (a – 2)(a + 2)(a2 + 4)


= (a2 – 22)(a2 + 4) [Taking a = a, and b = 2 in above identity]


= (a2 – 4)(a2 + 4)


= (a2)2 - 42 [Taking a = a2 and b = 4 in above identity]


= a4 – 16


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