Advertisements
Advertisements
Question
Expand the following, using suitable identity:
`[1/4a-1/2b+1]^2`
Advertisements
Solution
It is known that,
(x + y + z)2 = x2 + y2 + z2 + 2xy + 2yz + 2zx
`[1/4a - 1/2b + 1]^2`
= `(1/4a)^2 + (-1/2b)^2 + (1)^2 + 2(1/4a)(-1/2b) + 2(-1/2b)(1) + 2(1)(1/4a)`
= `1/16a^2 + 1/4b^2 + 1 - 1/4ab - b + 1/2a`
APPEARS IN
RELATED QUESTIONS
Use suitable identity to find the following product:
(3x + 4) (3x – 5)
Factorise the following using appropriate identity:
4y2 – 4y + 1
Expand the following, using suitable identity:
(–2x + 5y – 3z)2
Write the following cube in expanded form:
`[x-2/3y]^3`
Factorise:
27x3 + y3 + z3 – 9xyz
Evaluate following using identities:
991 ☓ 1009
Simplify the following:
322 x 322 - 2 x 322 x 22 + 22 x 22
Write in the expanded form:
(2a - 3b - c)2
Write in the expanded form: `(x/y + y/z + z/x)^2`
Write in the expanded form: `(x + 2y + 4z)^2`
Simplify of the following:
\[\left( x + \frac{2}{x} \right)^3 + \left( x - \frac{2}{x} \right)^3\]
Find the following product:
\[\left( \frac{x}{2} + 2y \right) \left( \frac{x^2}{4} - xy + 4 y^2 \right)\]
Find the following product:
If \[x^3 - \frac{1}{x^3} = 14\],then \[x - \frac{1}{x} =\]
If \[\frac{a}{b} + \frac{b}{a} = 1\] then a3 + b3 =
If a - b = 0.9 and ab = 0.36; find:
(i) a + b
(ii) a2 - b2.
Evaluate: (2 − z) (15 − z)
If `x^2 + (1)/x^2 = 18`; find : `x - (1)/x`
Simplify:
(2x + y)(4x2 - 2xy + y2)
If a + b + c = 0, then a3 + b3 + c3 is equal to ______.
