Question

factorise
$9x {}^{2} y { }^{2} - 16$
​

Answer 1

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$\: \: \: \: \: 9 {x^{2}{y }^{2} } \: - 16 \\ = {(3xy)}^{2} - {4}^{2} \\ = (3xy + 4)(3xy - 4)$

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Answer 2

9x²y² - 16 = (3xy + 4) (3xy - 4)

Step-by-step explanation:

We have to factorize (9x²y² - 16)

Now, 9x²y² - 16

= 3² * x²y² - 4², finding the perfect square forms

= (3xy)² - (4)², since a²b² = (ab)²

= (3xy + 4) (3xy - 4), since a² - b² = (a + b) (a - b)

This is the required factorization.

Note: In order to find factors of any algebraic polynomial containing 2 degree terms, we can use the method of finding roots: here we express the polynomial as an equation of a single variable and then we use quadratic formula or Sridhar Acharya's rule to find the value of the respective variable. Then we express it in a linear form containing x and y.

Reference:

• Factorize 20x^2-157x+222=0 [ https://brainly.in/question/9879718 ]