Factorise
25x2 + 16y2 + 4z2 - 40xy + 16yz - 20xz
25x2 + 16y2 + 4z2 - 40xy + 16yz - 20xz
25x2 + 16y2 + 4z2 - 40xy + 16yz - 20xz = 25x2 + 16y2 + 4z2 + (-40xy) + 16yz + (-20xz)
25x2 can be written as (-5x)2
16y2 can be written as (4y)2
4z2 can be written as (2z)2
-40xy can be written as 2(-5x)(4y)
16yz can be written as 2(4y)(2z)
-20xz can be written as 2(-5x)(2z)
⇒ 25x2 + 16y2 + 4z2 - 40xy + 16yz - 20xz = (-5x)2 + (4y)2 +
(2z)2 + 2(-5x)(4y) + 2(4y)(2z) + 2(-5x)(2z) …(i)
Using (a + b + c)2 = a2 + b2 + c2 + 2ab + 2bc + 2ca
Comparing (-5x)2 + (4y)2 + (2z)2 + 2(-5x)(4y) + 2(4y)(2z) + 2(-5x)(2z) with a2 + b2 + c2 + 2ab + 2bc + 2ca we get
a = -5x, b = 4y and c = 2z
therefore
(-5x)2 + (4y)2 + (2z)2 + 2(-5x)(4y) + 2(4y)(2z) + 2(-5x)(2z) = (- 5x + 4y + 2z)2
From (i)
25x2 + 16y2 + 4z2 - 40xy + 16yz - 20xz = (- 5x + 4y + 2z)2
Couldn't generate an explanation.
Generated by AI. May contain inaccuracies — always verify with your textbook.
