Advertisements
Advertisements
Question
Evaluate the following using identities:
`(a^2b - b^2a)^2`
Advertisements
Solution
In the given problem, we have to evaluate expressions by using identities.
The given expression is `(a^2b - b^2a)^2`
We shall use the identity `(x - y)^2 = x^2- 2xy + y^2`
Here `x = a^2b`
`y = b^2a`
By applying identity we get
`(a^2b - b^2a)^2 = (a^2b)^2 + (b^2a)^2 - 2 xx a^2b xx b^2a`
`= (a^2b xx a^2b) + (b^2a xx b^2a) - 2 xx a^2b xx b^2a`
`= a^4b^2 - 2a^3b^3 + b^4a^2`
Hence the value of `(a^2b - b^2a)^2 "is" a^4b^2 - 2a^3b^3 + b^4a^2`
APPEARS IN
RELATED QUESTIONS
Use suitable identity to find the following product:
(x + 4) (x + 10)
Evaluate the following product without multiplying directly:
104 × 96
Factorise the following using appropriate identity:
9x2 + 6xy + y2
Evaluate following using identities:
991 ☓ 1009
Write in the expanded form: (ab + bc + ca)2
Write in the expanded form:
`(a/(bc) + b/(ca) + c/(ab))^2`
Find the cube of the following binomials expression :
\[4 - \frac{1}{3x}\]
Evaluate of the following:
463+343
If x + \[\frac{1}{x}\] = then find the value of \[x^2 + \frac{1}{x^2}\].
Mark the correct alternative in each of the following:
If \[x + \frac{1}{x} = 5\] then \[x^2 + \frac{1}{x^2} = \]
(x − y) (x + y) (x2 + y2) (x4 + y4) is equal to ______.
Find the square of 2a + b.
Use the direct method to evaluate :
(0.5−2a) (0.5+2a)
Evaluate: (2a + 0.5) (7a − 0.3)
Expand the following:
(a + 4) (a + 7)
Expand the following:
(m + 8) (m - 7)
Evaluate, using (a + b)(a - b)= a2 - b2.
999 x 1001
If p2 + q2 + r2 = 82 and pq + qr + pr = 18; find p + q + r.
If `x/y + y/x = -1 (x, y ≠ 0)`, the value of x3 – y3 is ______.
Factorise the following:
16x2 + 4y2 + 9z2 – 16xy – 12yz + 24xz
