1.(iii) Use suitable identities to find the following product:

    (iii)    (3x+4)(3x - 5)

Answers (1)

We can write  (3x+4)(3x - 5)  as 

(3x+4)(3x - 5)= 9\left ( x+\frac{4}{3} \right )\left ( x-\frac{5}{3} \right )

We will use identity 

(x+a)(x+b)=x^2+(a+b)x+ab

Put   a = \frac{4}{3} \ \ and \ \ b = -\frac{5}{3}

9\left ( x+\frac{4}{3} \right )\left ( x-\frac{5}{3} \right )= 9\left ( x^2+\left ( \frac{4}{3}-\frac{5}{3} \right )x+\frac{4}{3} \times \left ( -\frac{5}{3} \right ) \right )
     
                                              =9x^2-3x-20

Therefore, (3x+4)(3x - 5)  is equal to  9x^2-3x-20

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