Question

Evaluate the product $95\times 96$ without multiplying directly

Answer 1

Given expression can be written as

$95\times 96=(100–5)\times (100–4)$

We know that

$(x–a)(x–b)=x^2–(a+b)x+ab$

Here

$x=100,a=5,b=4$

$$\begin{gathered} \Rightarrow (100–5)\times (100–4)={\left(100\right)}^2-(5+4)\times 100+(5\times 4) \\ =10000–900+20 \\ =9120 \end{gathered}$$

Hence the product is $9120$.