Using the formula a-b2-a2-2 a b-b2- evaluate-i 3102ii 5082iii 6302

(i) 3102=300+102=3002+2300 #215;10+102=90000+6000+100=96100 (ii) 5082=500+82=5002+2500 #215;8+82=250000+8000+64=258064 (iii) 6302=600+302=6002+2600 #215 ...

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Standard VIII

Mathematics

Distributive Property of Rational Numbers

Using the for...

Question

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

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Solution

(i) $310^{2} = {(300 + 10)}^{2} = (300^{2} + 2 (300 \times 10) + 10^{2}) = 90000 + 6000 + 100 = 96100$

(ii) $508^{2} = {(500 + 8)}^{2} = (500^{2} + 2 (500 \times 8) + 8^{2}) = 250000 + 8000 + 64 = 258064$

(iii) $630^{2} = {(600 + 30)}^{2} = (600^{2} + 2 (600 \times 30) + 30^{2}) = 360000 + 36000 + 900 = 396900$

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

Q. Find the square of 32 by using the formula

(a + b)^{2} = a^{2} + 2 a b + b^{2}

Find the squares of the following numbers using the formula.

(a + b)² = a² + 2ab + b²

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) $(a + b)^{2} = a^{2} + 2 a b - b^{2}$

Q. Question 3

Which of the following is correct?
a)

(a - b)^{2} = a^{2} + 2 a b - b^{2}

(a - b)^{2} = a^{2} - 2 a b + b^{2}

(a - b)^{2} = a^{2} - b^{2}

(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) (310)2 (ii) (508)2 (iii) (630)2

(i) 3102=300+102=3002+2300×10+102=90000+6000+100=96100 (ii) 5082=500+82=5002+2500×8+82=250000+8000+64=258064 (iii) 6302=600+302=6002+2600×30+302=360000+36000+900=396900

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