Advertisements
Advertisements
Question
Simplify the following expressions:
`(x + y - 2z)^2 - x^2 - y^2 - 3z^2 +4xy`
Advertisements
Solution
We have,
`(x + y - 2z)^2 - x^2 - y^2 - 3z^2 +4xy`
`=[x^2 + y^2 + (-2z)^2 + 2xy + 2(y)(-2z)] - x^2 - y^2 - 3z^2 + 4xy`
`= x^2 + y^2 + 4z^2 + 2xy - 4yz - x^2 - y^2 - 3z^2 = 4xy`
`= z^2 + 6xy - 4yz - 4zx`
`∴ (x + y - 2z)^2 - x^2 - y^2 - 3z^2 + 4xy = z^2 + 6xy - 4yz - 4zx`
APPEARS IN
RELATED QUESTIONS
Evaluate following using identities:
(a - 0.1) (a + 0.1)
Evaluate the following using identities:
(0.98)2
Simplify the following:
0.76 x 0.76 - 2 x 0.76 x 0.24 x 0.24 + 0.24
If 2x+3y = 13 and xy = 6, find the value of 8x3 + 27y3
Find the following product:
If x = 3 and y = − 1, find the values of the following using in identify:
\[\left( \frac{x}{7} + \frac{y}{3} \right) \left( \frac{x^2}{49} + \frac{y^2}{9} - \frac{xy}{21} \right)\]
If x = 3 and y = − 1, find the values of the following using in identify:
\[\left( \frac{x}{y} - \frac{y}{3} \right) \frac{x^2}{16} + \frac{xy}{12} + \frac{y^2}{9}\]
Find the following product:
(4x − 3y + 2z) (16x2 + 9y2 + 4z2 + 12xy + 6yz − 8zx)
If x + \[\frac{1}{x}\] = then find the value of \[x^2 + \frac{1}{x^2}\].
If \[x^2 + \frac{1}{x^2} = 102\], then \[x - \frac{1}{x}\] =
If a + b = 7 and ab = 10; find a - b.
If a - b = 0.9 and ab = 0.36; find:
(i) a + b
(ii) a2 - b2.
The number x is 2 more than the number y. If the sum of the squares of x and y is 34, then find the product of x and y.
Use the direct method to evaluate the following products :
(y + 5)(y – 3)
Evaluate: (2a + 0.5) (7a − 0.3)
Simplify by using formula :
(5x - 9) (5x + 9)
If p + q = 8 and p - q = 4, find:
pq
The coefficient of x in the expansion of (x + 3)3 is ______.
