Advertisements
Advertisements
Question
Simplify (2x + p - c)2 - (2x - p + c)2
Advertisements
Solution
We have
`(2x + p - c)^2 - (2x - p + c)^2`
`= [(2x)^2 + (p)^2 + (-c)^2 + 2(2x)(p) + 2(p)(-c) + 2(2x)(-c)] - [(2x)^2 + (-p)^2 + c^2 + 2(2x)(-p) + 2(2x)(c) + 2(-p)c]`
` =[4x^2 + p^2 + c^2 + 4xp - 2pc - 4cx] - [4x^2 + p^2 + c^2 - 4xp - 2pc + 4cx]`
`= 4x^2 + p^2 + c^2 + 4xp - 2pc - 4cx - 4x^2 - p^2 - c^2 + 4xp + 2pc - 4cx`
= 8xp - 8xc
= 8x(p - c)
`∴ (2x + p - c)^2 - (2x - p + c)^2 = 8x(p - c)`
APPEARS IN
RELATED QUESTIONS
Expand the following, using suitable identity:
(x + 2y + 4z)2
Evaluate the following using identities:
(1.5x2 − 0.3y2) (1.5x2 + 0.3y2)
Simplify the expression:
`(x + y + z)^2 + (x + y/2 + 2/3)^2 - (x/2 + y/3 + z/4)^2`
Find the cube of the following binomials expression :
\[\frac{3}{x} - \frac{2}{x^2}\]
If \[x - \frac{1}{x} = 7\], find the value of \[x^3 - \frac{1}{x^3}\].
Find the following product:
(4x − 5y) (16x2 + 20xy + 25y2)
Find the following product:
Evaluate:
253 − 753 + 503
If a + b + c = 9 and a2+ b2 + c2 =35, find the value of a3 + b3 + c3 −3abc
If a1/3 + b1/3 + c1/3 = 0, then
If 49a2 − b = \[\left( 7a + \frac{1}{2} \right) \left( 7a - \frac{1}{2} \right)\] then the value of b is
Evaluate: (2a + 0.5) (7a − 0.3)
Evaluate: 203 × 197
If `x + (1)/x = 3`; find `x^2 + (1)/x^2`
If p + q = 8 and p - q = 4, find:
pq
Simplify:
(7a +5b)2 - (7a - 5b)2
Simplify:
(1 + x)(1 - x)(1 - x + x2)(1 + x + x2)
Simplify:
(3x + 5y + 2z)(3x - 5y + 2z)
Which one of the following is a polynomial?
