factories 64x²-81y² pls give full explanation pls
Answers
Answered by
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
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)
Similar questions