Question

5. Factorise
257 16y +422 -- 40xy + 16yz - 204​

Answer 1

Factorise : 25x² + 16y² + 4z² - 40xy + 16yz - 20xz

⇒ 25x² = (-5x)² , 16y² = (4y)² , 4z² = (2z)² , -40xxy = 2(-5x)(4y) , 16yz = 2(4y)(2z) , -20xz = 2(-5x)(2z)

Comparing the given expression with x² + y² + z² + 2xy + 2yz + 2zx , we observe that x = -5x , y = 4y and z = 2z.

Using Identity : (x + y + z)² = x² + y² + z² + 2xy + 2yz + 2zx , we get

25x² + 16y² + 4z² - 40xy + 16yz - 20xz

= (-5x + 4y + 2z)² = (-5x)² + (4y)² + (2z)² + 2(-5x)(4y) + 2(4y)(2z) + 2(-5x)(2z)

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