Multiply:X2 + 4y2 + Z3 + 2xy + Xz − 2yz By X − 2y − Z - Mathematics

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Answer in Brief

Multiply: x2 + 4y2 + z3 + 2xy + xz − 2yz   by x − 2y − 

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Solution

 The given expression is

x2 + 4y2 + z3 + 2xy + xz − 2yz  

We have to multiply the above expression by. `(x-2y -z)`

The required product is

`(x-2y-z)(x^2 +4y^2 +z^2+2xy+ xz - 2yz)`

` = {x + (-2y)+(-z)}{(x)^2 +(-2y)^2 + (-z)^2 -x.(-2y) - (-2y).(-z) - (-z).x}`

Recall the formula

`a^3 +b^3 +c^3 -3abc = (a+b+c)(a^2 +b^2 +c^2 - ab - bc - ca)`

Using the above formula, we have

` = x^3 + ( -2y)^3 + (-z)^3 -3.x.(-2y).(-z)`

` = x^3 -8y^3 - z^3 - 6xyz`

  Is there an error in this question or solution?
Chapter 5: Factorisation of Algebraic Expressions - Exercise 5.4 [Page 23]

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RD Sharma Mathematics for Class 9
Chapter 5 Factorisation of Algebraic Expressions
Exercise 5.4 | Q 8.2 | Page 23

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