Question

Find factorisation

x⁴+2x²+9​

Answer 1

Formula used:

a² - b² = (a + b)(a - b)

a² + b² = (a + b)² - 2ab

Solutions:

x⁴ + 2x² + 9

(x²)² + (3)² - 2.x².3 + 2x²

(x² + 3)² - 6x² + 2x²

(x² + 3)² - (2x)²

(x² + 2x + 3)(x² - 2x + 3).

silentlover45.❤️

Answer 2

x⁴ + 2x² + 9 = (x² + 2x + 3)(x² - 2x + 3)

Given :

The expression x⁴ + 2x² + 9

To find :

To factorise the expression

Solution :

Step 1 of 2 :

Write down the given expression

The given expression is

x⁴ + 2x² + 9

Step 2 of 2 :

Factorise the expression

$\displaystyle \sf{ {x}^{4} + 2 {x}^{2} + 9}$

$\displaystyle \sf{ = {x}^{4} + 9 + 2 {x}^{2} }$

$\displaystyle \sf{ = {( {x}^{2} )}^{2} + {(3)}^{2} + 2. {x}^{2} .3 - 2. {x}^{2} .3+ 2 {x}^{2} }$

$\displaystyle \sf{ = {( {x}^{2} + 3 )}^{2} - 6 {x}^{2}+ 2 {x}^{2} }$

$\displaystyle \sf{ = {( {x}^{2} + 3 )}^{2} - 4 {x}^{2}}$

$\displaystyle \sf{ = {( {x}^{2} + 3 )}^{2} - {(2x)}^{2}}$

$\displaystyle \sf{ = ( {x}^{2} + 3 + 2x)( {x}^{2} + 3 - 2x)}$

$\displaystyle \sf{ = ( {x}^{2} + 2x + 3)( {x}^{2} - 2x + 3)}$

━━━━━━━━━━━━━━━━

Learn more from Brainly :-

$1.$ divide : (4x²- 100) ÷ 6(x+5)

https://brainly.in/question/15559404

2. Find the value of the expression a² – 2ab + b² for a = 1, b = 1

https://brainly.in/question/28961155