Question

Solve the following Equation:-

• 25a² + 28bc - 49c² - 4b²​

Answer 1

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Answer 2

ANSWER:

To Solve:

• 25a² + 28bc - 49c² - 4b²

Solution:

⇒ 25a² + 28bc - 49c² - 4b²

Rearranging the terms,

⇒ 25a² - 4b² - 49c² + 28bc

Taking (-) common from the terms after the 1st,

⇒ 25a² - (4b² + 49c² - 28bc)

⇒ 25a² - [(2b)² + (7c)² - 2(2b)(7c)]

As, (a² + b² - 2ab) = (a - b)²

So,

⇒ 25a² - (2b - 7c)²

⇒ (5a)² - (2b - 7c)²

We know that,

⇒ a² - b² = (a + b)(a - b)

So,

⇒ (5a - (2b - 7c)) × (5a + (2b - 7c))

⇒ (5a - 2b + 7c)(5a + 2b - 7c)

Formulae Used:

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