Question

factorise x²–y²/100 by using appropriate properties ​

Answer 1

Hii mate,

Just simple concept,

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$\bf \implies \: {x}^{2} - \frac{ {y}^{2} }{100} \\ \\ \bf \implies \: {x}^{2} - \left( \frac{y}{10} \right) ^{2} \\ \\ \bf \implies \: \left( {x} + \frac{y}{10} \right) \left({x} + \frac{y}{10} \right) \: \: \: \: \: \: \\ \\ \bf \: since \: \: {a}^{2} - {b}^{2} = (a + b)(a - b)$

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Additional information:

• (a+ b)² = a²+2ab +b²
• (a-b)² = a²-2ab +b²
• a²+b² = (a+b)(a-b)

Answer 2

Step-by-step explanation:

Hii mate,

Just simple concept,

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\begin{gathered}\bf \implies \: {x}^{2} - \frac{ {y}^{2} }{100} \\ \\ \bf \implies \: {x}^{2} - ( \frac{y}{10} ) ^{2} \\ \\ \bf \implies \: ( {x} + \frac{y}{10} ) ({x} + \frac{y}{10} ) \: \: \: \: \: \: \\ \\ \bf \: since \: \: {a}^{2} - {b}^{2} = (a + b)(a - b)\end{gathered}

⟹x

2

−

100

y

2

⟹x

2

−(

10

y

)

2

⟹(x+

10

y

)(x+

10

y

)

sincea

2

−b

2

=(a+b)(a−b)

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Additional information:

(a+ b)² = a²+2ab +b²

(a-b)² = a²-2ab +b²

a²+b² = (a+b)(a-b)