Math, asked by sreeja1235, 1 month ago

factories 64x²-81y² pls give full explanation pls​

Answers

Answered by shreyarath05
3

Answer:

So, we have 64x²-81y².

Now, 64x²=(8x) ² and 81y²=(9y) ²

We know a²-b²=(a+b) (a-b)

64x²-81y²=(8x+9y) (8x-9y).

Answered by Dinosaurs1842
4

Given :-

  • 64x² - 81y²

Aim :-

  • To factorize the question

Answer :-

Concept :-

Using the identity a² - b² = (a+b)(a-b) as both the terms are perfect squares

  • a = 8x
  • b = 9y

Here we say that a² - b² = (a+b)(a-b) as,

⇒ (a+b)(a-b)

By using the distributivity property,

⇒ a(a-b) + b(a-b)

⇒ a² - ab + ab + b²

Cancelling (-ab) and (+ab),

⇒ a² - b²

Solution :-

Hence,

⇒ 64x² = 8 × 8 × x × x

⇒ 8² × x²

⇒ 81y² = 9 × 9 × y × y

⇒ 9² × y²

Now that we know that the both the numbers are perfect squares,

By using the identity,

⇒ (8x)² - (9y)²

⇒ (8x - 9y)(8x + 9y)

Identities :-

  • (a+b)² = a² + 2ab + b²
  • (a-b)² = a² - 2ab + b²
  • (a+b+c)² = a² + b² + c² + 2ab + 2bc + 2ca
  • (x+a)(x+b) = x² + x(a+b) + ab
  • a²-b² = (a+b)(a-b)
  • (a+b)³ = a³ + 3a²b + 3ab² + b³
  • (a-b)³ = a³ - 3a²b + 3ab² - b³
  • a³+b³ = (a+b)(a² - ab + b²)
  • a³-b³ = (a-b)(a² + ab + b²)
  • a³+b³+c³ - 3abc = (a+b+c)(a² + b² + c² - ab - bc - ca)

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