Question

factorise the sum:
144x^2 - 289y^2​

Answer 1

Given :-

• 144x² - 289y²

Solution :-

Apply identity : a² - b² = (a + b)(a - b)

→ 144x² - 289y²

→ (12x)² - (17y)²

→ (12x + 17y)(12x - 17y)

Extra Information :-

• (a + b)² = a² + b² + 2ab
• (a - b)² = a² + b² - 2ab
• (a + b)³ = a³ + b³ + 3ab(a + b)
• (a - b)³ = a³ - b³ - 3ab(a - b)
• a³ - b³ = (a - b)(a² + ab + b²)
• a³ + b³ = (a + b)(a² - ab + b²)

Answer 2

Answer:-

➣

$\bf{(12x + 17y)(12x - 17y)}$

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• Given:-

$144x^2 - 289y^2$

• We know:-

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

Using the above Identity:-

$\longrightarrow{(12x)^2 - (17y)^2}$

$\longrightarrow{(12x + 17y)(12x - 17y)}$

Hence, Factorized

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Some Useful Identities:-

$\implies{(a+b)^2 = a^2 + b^2 + 2ab}$

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

$\implies{(a+b)^3 = a^3 + b^3 + 3ab(a + b)}$

$\implies{(a-b)^3 = a^3 - b^3 - 3ab(a-b)}$

$\implies{(a^3+b^3)= (a+b)(a^2 - ab + b^2)}$

$\implies{(a^3-b^3)= (a-b)(a^2 + ab + b^2)}$

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