Using the formula $(a - b)^{2} = (a^{2} - 2 a b + b^{2}),$ Evaluate:
(i) $(196)^{2}$
(ii) $(689)^{2}$
(iii) $(891)^{2}$

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Solution

We know that, $(a - b)^{2} = a^{2} - 2 a b + b^{2}$
(i) $(196)^{2} = (200 - 4)^{2}$
= $(200)^{2} - 2 \times 200 \times 4 + (4)^{2}$
=40000-1600+16
=40016-1600=38416
(ii) $(689)^{2} = (700 - 11)^{2}$
= $(700)^{2} - 2 \times 700 \times 11 + (11)^{2}$
=490000-15400+121
=490121-15400=474721
(iii) $(891)^{2} = (900 - 9)^{2}$
= $(900)^{2} - 2 \times 900 \times 9 + (9)^{2}$
=810000-16200+81
=810081-16200=793881

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Q. Using the formula (a − b)² = (a² − 2ab + b²), evaluate:
(i) (196)²
(ii) (689)²
(iii) (891)²

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Which of the following is correct?
a) $(a - b)^{2} = a^{2} + 2 a b - b^{2}$
b) $(a - b)^{2} = a^{2} - 2 a b + b^{2}$
c) $(a - b)^{2} = a^{2} - b^{2}$
d) $(a + b)^{2} = a^{2} + 2 a b - b^{2}$

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Using the formula (a−b)2=(a2−2ab+b2), Evaluate: (i) (196)2 (ii) (689)2 (iii) (891)2

We know that, (a−b)2=a2−2ab+b2 (i) (196)2=(200−4)2 =(200)2−2×200×4+(4)2 =40000-1600+16 =40016-1600=38416 (ii) (689)2=(700−11)2 =(700)2−2×700×11+(11)2 =490000-15400+121 =490121-15400=474721 (iii) (891)2=(900−9)2 =(900)2−2×900×9+(9)2 =810000-16200+81 =810081-16200=793881

Using the formula $(a - b)^{2} = (a^{2} - 2 a b + b^{2}),$ Evaluate:
(i) $(196)^{2}$
(ii) $(689)^{2}$
(iii) $(891)^{2}$