Advertisements
Advertisements
Question
Expand the following, using suitable identity:
(–2x + 3y + 2z)2
Advertisements
Solution
It is known that,
(x + y + z)2 = x2 + y2 + z2 + 2xy + 2yz + 2zx
(–2x + 3y + 2z)2 = (–2x)2 + (3y)2 + (2z)2 + 2(–2x)(3y) + 2(3y)(2z) + 2(2z)(–2x)
= 4x2 + 9y2 + 4z2 – 12xy + 12yz – 8xz
APPEARS IN
RELATED QUESTIONS
Evaluate the following product without multiplying directly:
103 × 107
If x + y + z = 0, show that x3 + y3 + z3 = 3xyz.
If 9x2 + 25y2 = 181 and xy = −6, find the value of 3x + 5y
If 3x - 7y = 10 and xy = -1, find the value of `9x^2 + 49y^2`
Write the expanded form:
`(-3x + y + z)^2`
Write in the expanded form: `(x + 2y + 4z)^2`
Find the cube of the following binomials expression :
\[4 - \frac{1}{3x}\]
If \[x^2 + \frac{1}{x^2}\], find the value of \[x^3 - \frac{1}{x^3}\]
Find the following product:
\[\left( 3 + \frac{5}{x} \right) \left( 9 - \frac{15}{x} + \frac{25}{x^2} \right)\]
If \[a^2 + \frac{1}{a^2} = 102\] , find the value of \[a - \frac{1}{a}\].
\[\frac{( a^2 - b^2 )^3 + ( b^2 - c^2 )^3 + ( c^2 - a^2 )^3}{(a - b )^3 + (b - c )^3 + (c - a )^3} =\]
Evaluate : (4a +3b)2 - (4a - 3b)2 + 48ab.
Use the direct method to evaluate the following products:
(x + 8)(x + 3)
Use the direct method to evaluate the following products :
(3x – 2y) (2x + y)
Find the squares of the following:
3p - 4q2
Find the squares of the following:
(2a + 3b - 4c)
Simplify by using formula :
(5x - 9) (5x + 9)
Simplify:
(2x - 4y + 7)(2x + 4y + 7)
Factorise the following:
25x2 + 16y2 + 4z2 – 40xy + 16yz – 20xz
Multiply x2 + 4y2 + z2 + 2xy + xz – 2yz by (–z + x – 2y).
