Advertisements
Advertisements
Question
Factorise the following:
9x2 + 4y2 + 16z2 + 12xy – 16yz – 24xz
Advertisements
Solution
9x2 + 4y2 + 16z2 + 12xy – 16yz – 24xz
= (3x)2 + (2y)2 + (–4z)2 + 2(3x)(2y) + 2(2y)(–4z) + 2(–4z)(3x) ...[Using identity, (a + b + c)2 = a2 + b2 + c2 + 2ab + 2bc + 2ca]
= (3x + 2y – 4z)2
= (3x + 2y – 4z)(3x + 2y – 4z)
APPEARS IN
RELATED QUESTIONS
Write the following cube in expanded form:
`[3/2x+1]^3`
Factorise the following:
64m3 – 343n3
What are the possible expressions for the dimensions of the cuboids whose volume is given below?
| Volume : 3x2 – 12x |
If 9x2 + 25y2 = 181 and xy = −6, find the value of 3x + 5y
Simplify the following products:
`(x^3 - 3x^2 - x)(x^2 - 3x + 1)`
Write the expanded form:
`(-3x + y + z)^2`
If 3x − 2y = 11 and xy = 12, find the value of 27x3 − 8y3
Evaluate of the following:
(99)3
Simplify of the following:
\[\left( x + \frac{2}{x} \right)^3 + \left( x - \frac{2}{x} \right)^3\]
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:
\[\left( \frac{x}{y} - \frac{y}{3} \right) \frac{x^2}{16} + \frac{xy}{12} + \frac{y^2}{9}\]
If x = −2 and y = 1, by using an identity find the value of the following
If \[x + \frac{1}{x} = 3\] then find the value of \[x^6 + \frac{1}{x^6}\].
If the volume of a cuboid is 3x2 − 27, then its possible dimensions are
Use the direct method to evaluate :
`(3/5"a"+1/2)(3/5"a"-1/2)`
If x + y = 1 and xy = -12; find:
x - y
If `"a"^2 + (1)/"a"^2 = 14`; find the value of `"a" + (1)/"a"`
Simplify:
(4x + 5y)2 + (4x - 5y)2
The value of 2492 – 2482 is ______.
Find the following product:
`(x/2 + 2y)(x^2/4 - xy + 4y^2)`
