Question

Factorise 9x^2 + 2 + 1/9x^2

Answer 1

$\textsf{\large{\underline{Solution}:}}$

We have to factorise the given polynomial.

$\rm = 9 {x}^{2} + 2 + \dfrac{1}{9 {x}^{2} }$

We can write it as:

$\rm = {(3x)}^{2} + 2 \times (3x) \times \dfrac{1}{3x} + { \bigg( \dfrac{1}{3x} \bigg)}^{2}$

We know that:

$\rm : \longmapsto {x}^{2} + 2xy + {y}^{2} = {(x + y)}^{2}$

Therefore, the polynomial becomes:

$\rm = { \bigg( 3x + \dfrac{1}{3x} \bigg)}^{2}$

★ Hence, the factorisation of the given polynomial is (3x + 1/3x)²

$\textsf{\large{\underline{More To Know}:}}$

• (a + b)² = a² + 2ab + b²
• (a - b)² = a² - 2ab + b²
• a² - b² = (a + b)(a - b)
• (a + b)³ = a³ + 3ab(a + b) + b³
• (a - b)³ = a³ - 3ab(a - b) - b³
• a³ + b³ = (a + b)(a² - ab + b²)
• a³ - b³ = (a - b)(a² + ab + b²)
• (x + a)(x + b) = x² + (a + b)x + ab
• (x + a)(x - b) = x² + (a - b)x - ab
• (x - a)(x + b) = x² - (a - b)x - ab
• (x - a)(x - b) = x² - (a + b)x + ab

Answer 2

Answer:

How to solve your problem

9 2 + 2 + 1 9 ⋅ 2

Step-by-step explanation:

9

2

+

2

+

1

9

2

9x^{2}+2+\frac{1}{9}x^{2}

9x2+2+91​x2