Question

Compute the following differences $(10.3\times 9.7)-(10.7\times 9.3)$

• A. 0.2
• B. 0.4
• C. 0.8
• D. 0.6

Answer 1

Answer: (B)

($0.4$)

The given expression is $(10.3\times 9.7)-(10.7\times 9.3)$

$=(10+0.3)(10-0.3)-(10+0.7)(10-0.7)$
Use the formula of $(a+b)(a-b)=a^2-b^2$, we get

$=\left[\right(10{)}^2-\left(0.3{)}^2\right]-\left[\right(10{)}^2-\left(0.7{)}^2\right]$

$={10}^2-(0.3{)}^2-{10}^2+(0.7{)}^2$

$=(0.7{)}^2-(0.3{)}^2$

$=(0.7+0.3)(0.7-0.3)$ [From, the formula of $(a+b)(a-b)=a^2-b^2$]

$=1\times 0.4$

$=0.4$