Question

Factorize using identities
i) 9x² - 16 y²
ii) 16x²y² + 1 – 8xy

Answer 1

Answer:

1) Using:a2−b2=(a+b)(a−b)

Using the above identity, the equation 9x2−16y2 can be factorised as follows:

9x2−16y2=(3x)2−(4y)2=(3x+4y)(3x−4y)

Hence, 9x2−16y2=(3x+4y)(3x−4y)

2): "y2"   was replaced by   "y^2".  1 more similar replacement(s).

STEP1:Equation at the end of step 1

(1 - 8xy) + (24x2 • y2)

STEP2:Trying to factor a multi variable polynomial

 2.1    Factoring    16x2y2 - 8xy + 1 

Try to factor this multi-variable trinomial using trial and error 

 Found a factorization  :  (4xy - 1)•(4xy - 1)

Detecting a perfect square :

 2.2    16x2y2  -8xy  +1  is a perfect square 

 It factors into  (4xy-1)•(4xy-1)

which is another way of writing  (4xy-1)2

How to recognize a perfect square trinomial:  

 • It has three terms  

 • Two of its terms are perfect squares themselves  

 • The remaining term is twice the product of the square roots of the other two terms

Final result :

(4xy - 1)2

Step-by-step explanation:

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Answer 2

Step-by-step explanation:

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