Advertisements
Advertisements
Question
Simplify (5x – 3y)2 – (5x + 3y)2
Advertisements
Solution
We have the identities
(a + b)2 = a2 + 2ab + b2
(a – b)2 = a2 – 2ab + b2
So (5x – 3y)2 – (5x + 3y)2 = (5x)2 – (2 × 5x × 3y) + (3y)2
= 52x2 – 30xy + 32y2 – [52x2 – 30xy + 32y2]
= 25x2 – 30xy + 9y2 – [25x2 + 30xy + 9y2]
= 25x2 – 30xy + 9y2 – 25x2 – 30xy – 9y2
= x2(25 – 25) – xy(30 + 30) + y2(9 – 9)
= 0x2 – 60xy + 0y2 = – 60xy
∴ (5x – 3y)2 – (5x + 3y)2 = – 60xy
APPEARS IN
RELATED QUESTIONS
The product of (x + 5) and (x – 5) is ____________
Using the identity (a + b)(a – b) = a2 – b2, find the following product
(6x + 7y)(6x – 7y)
(5 + 20)(–20 – 5) = ?
a2 – b2 = (a + b) ______.
Using suitable identities, evaluate the following.
(339)2 – (161)2
Factorise the following using the identity a2 – b2 = (a + b)(a – b).
4x2 – 49y2
Factorise the following using the identity a2 – b2 = (a + b)(a – b).
`y^3 - y/9`
Factorise the following using the identity a2 – b2 = (a + b)(a – b).
`1/36a^2b^2 - 16/49b^2c^2`
Factorise the following using the identity a2 – b2 = (a + b)(a – b).
x4 – 1
Verify the following:
(p – q)(p2 + pq + q2) = p3 – q3
