Question

81(a-b)²-36(a+b)² factories answer is 9(5a-b)(a-5b)​ which formula is used​

Answer 1

Answer:

81(a-b)²-36(a+b)²

=9(5a-b)(a-5b)

Step-by-step explanation:

81(a-b)²-36(a+b)²

= [9(a-b)]²-[6(a+b)]²

= (9a-9b)²-(6a+6b)²

= [(9a-9b)+(6a+6b)][(9a-9b)-(6a+6b)]

/* By algebraic identity:

x²-y² = (x+y)(x-y) */

= (9a-9b+6a+6b)(9a-9b-6a-6b)

= (9a+6a-9b+6b)(9a-6a-9b-6b)

= (15a-3b)(3a-15b)

= [3(5a-b)][3(a-5b)]

= 9(5a-b)(a-5b)

Therefore,.

81(a-b)²-36(a+b)²

=9(5a-b)(a-5b)

•••♪

Answer 2

9 (5a - b) (a - 5b)

Step-by-step explanation:

Given,

81(a - b)² - 36(a + b)²

[9(a - b)]² - [6(a + b)]²

Substituting the formula: a² - b² = (a + b) (a - b)

[9(a - b) + [6(a + b)] [9(a - b) - [6(a + b)]

[ (9a - 9b) + (6a + 6b)] [ (9a - 9b) - (6a + 6b)]

(9a - 9b + 6a + 6b) (9a - 9b - 6a - 6b)

(15a - 3b) (3a - 15b)

Taking out 3 as common:

3 (5a - b) 3 (a - 5b)

Multiplying 3 and 3:

9 (5a - b) (a - 5b)

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