Browse by Stream
QnA
Home
QnA
Go To Your Study Dashboard

Get Answers to all your Questions

header-bg qa
  • Home
  • NCERT
  • Find the following product (i) \left (\frac{x}{2}+2y \right )\left ( \frac{x^{2}}{4}-xy+4y^{2} \right ) (ii) (x^{2}-1)(x^{4}+x^{2}+1)

Find the following product

(i) \left (\frac{x}{2}+2y \right )\left ( \frac{x^{2}}{4}-xy+4y^{2} \right )

(ii) (x^{2}-1)(x^{4}+x^{2}+1)

Answers (1)

(i)      \frac{x^{3}}{8}+8y^{3}

Given: \left (\frac{x}{2}+2y \right )\left ( \frac{x^{2}}{4}-xy+4y^{2} \right )

=\frac{x}{2}\left ( \frac{x^{2}}{4}-xy+4y^{2} \right )+2y \left ( \frac{x^{2}}{4}-xy+4y^{2} \right )\\ =\frac{x^{3}}{8}-\frac{x^{2}y}{2}+\frac{4xy^{2}}{2}+\frac{2yx^{2}}{4}-2xy^{2}+8y^{3}\\ =\frac{x^{3}}{8}-\frac{x^{2}y}{2}+\frac{x^{2}y}{2}+2xy^{2}-2xy^{2}+8y^{3}\\ =\frac{x^{3}}{8}+8y^{3}

(ii) x^{6}-1

Given (x^{2}-1)(x^{4}+x^{2}+1)

=x^{2}(x^{4}+x^{2}+1)-1(x^{4}+x^{2}+1)\\ =x^{6}+x^{4}+x^{2}-x^{2}-x^{4}-x^{2}-1\\ =x^{6}-1

 

Posted by

infoexpert24

View full answer

Similar Questions

Latest Question