Giải bài 18 trang 14

Đề bài

Tính nhanh:

a) ${202}^2$

b) $299.301$

c) ${95}^3+{15.95}^2+\mathrm{3.95.25}+5^3$

d) $9\left({10}^2+10+1\right)+100\left({98}^2+392+2^2\right)$

Lời giải chi tiết

a) ${202}^2={\left(200+2\right)}^2={200}^2+\mathrm{2.200.2}+2^2=40000+800+4=40804$

b) $299.301=\left(300-1\right)\left(300+1\right)={300}^2-1=90000-1=89999$

c) $\begin{array}{c}{95}^3+{15.95}^2+\mathrm{3.95.25}+5^3\\ ={95}^3+{3.95}^2.5+{\mathrm{3.95.5}}^2+5^3={\left(95+5\right)}^3={100}^3=1000000\end{array}$

d) $\begin{array}{c}9\left({10}^2+10+1\right)+100\left({98}^2+392+2^2\right)\\ =\left(10-1\right)\left({10}^2+10+1\right)+100\left({98}^2+\mathrm{2.98.2}+2^2\right)={10}^3-1+100{\left(98+2\right)}^2\\ =1000-1+{100.100}^2=999+100.10000=999+1000000=1000999\end{array}$