Using the formula $(a + b)^{2} = (a^{2} + 2 a b + b^{2}$ , evaluate:
(i) $(310)^{2}$
(ii) $(508)^{2}$
(iii) $(630)^{2}$

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Solution

We know that $(a + b)^{2} = (a^{2} + 2 a b + b^{2}$
(i) $(310)^{2} = (300 + 10)^{2}$
= $(300)^{2} + 2 \times 300 \times 10 + (10)^{2}$
=90000+6000+100=96100
(ii) $(508)^{2} = (500 + 8)^{2}$
$(500)^{2} + 2 \times 500 \times 8 + (8)^{2}$
$250000 + 8000 + 64 = 258064$ (iii) $(630)^{2} = (600 + 30)^{2}$
= $(600)^{2} + 2 \times 600 \times 30 + (30)^{2}$
=360000+36000+900=396900

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Using the formula (a+b)2=(a2+2ab+b2, evaluate: (i) (310)2 (ii) (508)2 (iii) (630)2

We know that (a+b)2=(a2+2ab+b2 (i) (310)2=(300+10)2 =(300)2+2×300×10+(10)2 =90000+6000+100=96100 (ii) (508)2=(500+8)2 (500)2+2×500×8+(8)2 250000+8000+64=258064 (iii) (630)2=(600+30)2 =(600)2+2×600×30+(30)2 =360000+36000+900=396900

Using the formula $(a + b)^{2} = (a^{2} + 2 a b + b^{2}$ , evaluate:
(i) $(310)^{2}$
(ii) $(508)^{2}$
(iii) $(630)^{2}$