Using the formula for squaring a binomial, evaluate the following:

Question:

Using the formula for squaring a binomial, evaluate the following:

(i) (54)2

(ii) (82)2

(iii) (103)2

(iv) (704)2

Solution:

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

(i)  $(54)^{2}$

$=(50+4)^{2}$

$=(50)^{2}+2 \times 50 \times 4+(4)^{2}$

$=2500+400+16$

$=2916$

(ii) $(82)^{2}$

$=(80+2)^{2}$

$=(80)^{2}+2 \times 80 \times 2+(2)^{2}$

$=6400+320+4$

$(82)^{2}$

$=(80+2)^{2}$

$=(80)^{2}+2 \times 80 \times 2+(2)^{2}$

$=6400+320+4$

$=6724$$=6724$

(iii) $(103)^{2}$

$=(100+3)^{2}$

$=(100)^{2}+2 \times 100 \times 3+(3)^{2}$

$=10000+600+9$

$=10609$

(iv) $(704)^{2}$

$=(700+4)^{2}$

$=(700)^{2}+2 \times 700 \times 4+(4)^{2}$

$=490000+5600+16$

$=495616$

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