Question

Using the formula for squaring a binomial, evaluate the following:
(i) (54)²
(ii) (82)²
(iii) (103)²
(iv) (704)²

Answer 1

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

(i)
$$\begin{gathered} {\left(54\right)}^2 \\ =(50+4{)}^2 \\ ={\left(50\right)}^2+2\times 50\times 4+{\left(4\right)}^2 \\ =2500+400+16 \\ =2916 \end{gathered}$$

(ii)
$$\begin{gathered} {\left(82\right)}^2 \\ =(80+2{)}^2 \\ ={\left(80\right)}^2+2\times 80\times 2+{\left(2\right)}^2 \\ =6400+320+4 \\ =6724 \end{gathered}$$

(iii)
$$\begin{gathered} {\left(103\right)}^2 \\ =(100+3{)}^2 \\ ={\left(100\right)}^2+2\times 100\times 3+{\left(3\right)}^2 \\ =10000+600+9 \\ =10609 \end{gathered}$$

(iv)
$$\begin{gathered} {\left(704\right)}^2 \\ =(700+4{)}^2 \\ ={\left(700\right)}^2+2\times 700\times 4+{\left(4\right)}^2 \\ =490000+5600+16 \\ =495616 \end{gathered}$$