Question

Evaluate the product without multiplying directly : 104×97.

Answer 1

Let us find the product 104 × 97 using the identity $\left(x+a\right)\left(x-b\right)=x^2+\left(a-b\right)x-ab$.
$$\begin{gathered} 104\times 97=\left(100+4\right)\left(100-3\right) \\ ={\left(100\right)}^2+\left(4-3\right)\times 100-4\times 3\left[\because \left(x+a\right)\left(x-b\right)=x^2+\left(a-b\right)x-ab\right] \\ =10000+100-12 \\ =10088 \end{gathered}$$
Hence, 104 × 97 = 10088.