Advertisements
Advertisements
Question
Factorise the following:
`(2x + 1/3)^2 - (x - 1/2)^2`
Advertisements
Solution
`(2x + 1/3)^2 - (x - 1/2)^2 = [(2x + 1/3) - (x - 1/2)][(2x + 1/3) + (x - 1/2)]`
= `(2x - x + 1/3 + 1/2)(2x + x + 1/3 - 1/2)` ...[Using identity, a2 – b2 = (a – b)(a + b)]
= `(x + (2 + 3)/6)(3x + (2 - 3)/6)`
= `(x + 5/6)(3x - 1/6)`
APPEARS IN
RELATED QUESTIONS
Write the following cube in expanded form:
(2x + 1)3
If `x^2 + 1/x^2 = 66`, find the value of `x - 1/x`
Write in the expanded form:
`(a + 2b + c)^2`
Write in the expanded form:
`(2 + x - 2y)^2`
If x = 3 and y = − 1, find the values of the following using in identify:
\[\left( \frac{5}{x} + 5x \right)\] \[\left( \frac{25}{x^2} - 25 + 25 x^2 \right)\]
If \[x + \frac{1}{x} = 3\] then find the value of \[x^6 + \frac{1}{x^6}\].
If \[x - \frac{1}{x} = \frac{1}{2}\],then write the value of \[4 x^2 + \frac{4}{x^2}\]
If \[x^2 + \frac{1}{x^2} = 102\], then \[x - \frac{1}{x}\] =
If \[x^3 + \frac{1}{x^3} = 110\], then \[x + \frac{1}{x} =\]
If \[3x + \frac{2}{x} = 7\] , then \[\left( 9 x^2 - \frac{4}{x^2} \right) =\]
Use identities to evaluate : (97)2
Evaluate: (6 − 5xy) (6 + 5xy)
Find the squares of the following:
`(7x)/(9y) - (9y)/(7x)`
Evaluate the following without multiplying:
(999)2
Evaluate, using (a + b)(a - b)= a2 - b2.
4.9 x 5.1
If p + q = 8 and p - q = 4, find:
pq
If m - n = 0.9 and mn = 0.36, find:
m2 - n2.
Simplify:
`("a" - 1/"a")^2 + ("a" + 1/"a")^2`
Simplify:
(x + y - z)2 + (x - y + z)2
Simplify:
(2x + y)(4x2 - 2xy + y2)
