Question

Using the formula for squaring a binomial, evaluate the following:
(i) (69)²
(ii) (78)²
(iii) (197)²
(iv) (999)²

Answer 1

We shall use the identity (a-b)² = a² +b² -2ab.

(i)
$$\begin{gathered} {\left(69\right)}^2 \\ =(70-1{)}^2 \\ ={\left(70\right)}^2-2\times 70\times 1+1 \\ =4900-140+1 \\ =4761 \end{gathered}$$

(ii)
$$\begin{gathered} {\left(78\right)}^2 \\ =(80-2{)}^2 \\ ={\left(80\right)}^2-2\times 80\times 2+4 \\ =6400-320+4 \\ =6084 \end{gathered}$$

(iii)
$$\begin{gathered} {\left(197\right)}^2 \\ =(200-3{)}^2 \\ ={\left(200\right)}^2-2\times 200\times 3+9 \\ =40000-1200+9 \\ =38809 \end{gathered}$$

(iv)
$$\begin{gathered} {\left(999\right)}^2 \\ =(1000-1{)}^2 \\ ={\left(1000\right)}^2-2\times 1000\times 1+1 \\ =1000000-2000+1 \\ =998001 \end{gathered}$$