Q : 1    Use a suitable identity to get each of the following product.

          (ix)   (\frac{x}{2}+ \frac{3y}{4})(\frac{x}{2}+ \frac{3y}{4})

Answers (1)

(\frac{x}{2}+ \frac{3y}{4}) \times (\frac{x}{2}+ \frac{3y}{4}) = (\frac{x}{2}+ \frac{3y}{4})^{2}

We use identity I for this which is 
                                                      (a+b)^{2} =a^{2}+2ab + b^{2}
In this a = \frac{x}{2} and b = \frac{3y}{4}
                                                  

                                           (\frac{x}{2}+ \frac{3y}{4})^{2} = (\frac{x}{2})^{2} + 2 (\frac{x}{2})(\frac{3y}{4}) + (\frac{3y}{4})^{2}
                                                                   =  \frac{x^{2}}{4} + \frac{3xy}{4} + \frac{9y^{2}}{16}

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