Question

Express (x2 – 4x + 9)(x2 + 4x – 9) as a difference of two square.​

Answer 1

Explanation:

Answer

4(x+2y)(2x+y)

=4(2x 2 +xy+4xy+2y 2 )

=4(2x 2 +2y 2+4xy+xy)

=4(2(x 2 +y 2+2xy)+xy)

=4(2(x+y) 2+xy)

=8(x+y) 2 +4xy

=8(x+y) 2+(x+y) 2 −(x−y) 2

[∵4xy=(x+y) 2−(x−y) 2 ]

=9(x+y) 2−(x−y) 2

=[3(x+y)] 2 −(x−y) 2

The solution of this question.

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Answer 2

Answer:

The given expression as difference of two squares is ( x² )² - ( 4x - 9 )².

Step-by-step-explanation:

We have to express ( x² - 4x + 9 ) ( x² + 4x - 9 ) as a difference of two squares.

Now, by simplifying the given expression, we get,

( x² - 4x + 9 ) ( x² + 4x - 9 )

⇒ x² ( x² + 4x - 9 ) - 4x ( x² + 4x - 9 ) + 9 ( x² + 4x - 9 )

⇒ x⁴ + 4x³ - 9x² - ( 4x³ + 16x² - 36x ) + 9x² + 36x - 81

⇒ x⁴ + 4x³ - 9x² - 4x³ - 16x² + 36x + 9x² + 36x - 81

⇒ x⁴ + 4x³ - 4x³ - 9x² + 9x² - 16x² + 36x + 36x - 81

⇒ x⁴ - 16x² + 36x + 36x - 81

⇒ x⁴ - 16x² + 72x - 81

⇒ x⁴ - ( 16x² - 72x + 81 )

⇒ x⁴ - [ ( 4x )² - 4 * 9 * 2 x + 9² ]

⇒ ( x² )² - ( 4x - 9 )²

∴ The given expression as difference of two squares is ( x² )² - ( 4x - 9 )².