Question

find the following using identities:- a. (155)²
b. (12)²-(10)²
c.(180)²

Answer 1

Your answer is here!!!!!
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{a}- (155)².
= (150+5)². compare with(a+b)²= a²+b²+2ab
= (150)²+(5)²+2×150×5
= 22500+25+1500
= 24025. ans

{b}- (12)²-(10)²
= (12)²-(10)². compare with a²-b² = (a+b)(a-b)
= (12+10)(12-10)
= (22)(2)
= 44. ans

{c}- (180)²
= (100+80)². compare with(a+b)²= a²+b²+2ab
= (100)²+(80)²+2×100×80
= 10000+6400+16000
= 32400. ans
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Answer 2

$a. {(155)}^{2} = (100 + 55) {}^{2} \\ (x + y) {}^{2} = {x}^{2} + {y}^{2} + 2 xy \\ {(100 + 55)}^{2} \\ = 100 {}^{2} + {55}^{2} + 2 \times 100 \times 55 \\ = 10000 + 3025 + 11000 \\ = 24025$


$b. \: \: {(12)}^{2} - {(10)}^{2} \\ {x}^{2} - {y}^{2} = (x + y)(x - y) \\ = (12 + 10)(12 - 10) \\ = 22 \times 2 \\ = 44$

$c. \: \: (180) {}^{2} = (200 - 20) {}^{2} \\ (x - y) {}^{2} = {x}^{2} + {y}^{2} - 2 xy \\ (200 - 20) {}^{2} \\ = {200}^{2} + {20}^{2} - 2 \times 200 \times 20 \\ = 40000 + 400 - 8000 \\ = 32400$