Advertisements
Advertisements
Question
Multiply x2 + 4y2 + z2 + 2xy + xz – 2yz by (–z + x – 2y).
Advertisements
Solution
According to the question:
(x2 + 4y2 + z2 + 2xy + xz – 2yz) × (–z + x – 2y)
Now, multiply as follows:
= {x + (–2y) + (–z)}{(x)2 + (–2y)2 + (–z2) – (x)(–2y) – (–2y)(–z) – (–z)(x)}
= x3 + (–2y)3 + (–z)3 – 3 × x × (–2y) × (–z)
Use the identity:
(a + b + c)(a2 + b2 + c2 – ab – bc – ca) = a3 + b3 + c3 – 3abc
= x3 – 8y3 – z3 – 6xyz
APPEARS IN
RELATED QUESTIONS
Use suitable identity to find the following product:
`(y^2+3/2)(y^2-3/2)`
Expand the following, using suitable identity:
(–2x + 5y – 3z)2
Factorise:
`2x^2 + y^2 + 8z^2 - 2sqrt2xy + 4sqrt2yz - 8xz`
Evaluate the following using suitable identity:
(102)3
Factorise:
27x3 + y3 + z3 – 9xyz
If x + y + z = 0, show that x3 + y3 + z3 = 3xyz.
What are the possible expressions for the dimensions of the cuboids whose volume is given below?
| Volume : 12ky2 + 8ky – 20k |
Evaluate the following using identities:
(2x + y) (2x − y)
Find the cube of the following binomials expression :
\[2x + \frac{3}{x}\]
Simplify of the following:
\[\left( x + \frac{2}{x} \right)^3 + \left( x - \frac{2}{x} \right)^3\]
If \[x^4 + \frac{1}{x^4} = 119\] , find the value of \[x^3 - \frac{1}{x^3}\]
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 a + b = 10 and ab = 16, find the value of a2 − ab + b2 and a2 + ab + b2
If a − b = 5 and ab = 12, find the value of a2 + b2
If the volume of a cuboid is 3x2 − 27, then its possible dimensions are
The difference between two positive numbers is 5 and the sum of their squares is 73. Find the product of these numbers.
If `"a" - 1/"a" = 10`; find `"a"^2 - 1/"a"^2`
Simplify:
(2x - 4y + 7)(2x + 4y + 7)
Find the value of x3 + y3 – 12xy + 64, when x + y = – 4
Prove that (a + b + c)3 – a3 – b3 – c3 = 3(a + b)(b + c)(c + a).
