# 1.(iii) Use suitable identities to find the following product:    (iii)    $(3x+4)(3x - 5)$

G Gautam harsolia

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

$\dpi{100} 9\left ( x+\frac{4}{3} \right )\left ( x-\frac{5}{3} \right )= 9\left ( x^2+\left ( \frac{4}{3}-\frac{5}{3} \right )x+\frac{4}{3} \times \left ( -\frac{5}{3} \right ) \right )$

$=9x^2-3x-20$

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

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