Question

Factorise : 9x^- 9(a+B)x+ 2a^+5ab+2b^

Please explain it with Reasons

Answer 1

The answer is given below :

Now,

9x² - 9(a + b)x + 2a² + 5ab + 2b²

= 9x² - 9(a + b)x + (2a² + 4ab + ab + 2b²)

= 9x² - 9(a + b)x + {2a(a + 2b) + b(a + 2b)}

= 9x² - 9(a + b)x + (a + 2b)(2a + b) .....(i)

Here,

(2a + b) + (a + 2b) = 3(a + b)

Then, next of (i) is

= 9x² - 3{(2a + b) + (a + 2b)}x + (a + 2b)(2a + b)

= 9x² - 3(2a + b)x - 3(a + 2b)x + (a + 2b)(2a + b)

=3x(3x - 2a - b) - (a + 2b)(3x - 2a - b)

= (3x - 2a - b)(3x - a - 2b),

which is the required factorization.

Thank you for your question.