Question

can we factorise 4x^2+9y^2+16z^2+12xy-24xz-16xz
as (-2x^2-3y^2+4z^2)

Answer 1

Answer:

Identity:

An identity is an equality which is true for all values of a variable in the equality.

(a + b + c)² = a² + b² + c² + 2ab + 2bc + 2ca

In an identity the right hand side expression is called expanded form of the left hand side expression.

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Solution:

(i) 4x²+9y²+16z²+12xy–24yz–16xz

We can we write the given expression as

 

=(2x)²+(3y)²+(−4z)²+(2×2x×3y)+(2×3y×−4z)+(2×−4z×2x)

 

=(2x+3y–4z)²

Identity used:

[a²+b²+c²+2ab+2bc+2ca = (a²+b²+c²)]

 

=(2x+3y–4z) (2x+3y–4z)

 

(ii) 2x²+y²+8z²–2√2xy+4√2yz–8xz

 

We can rewrite the given expression as

=(−√2x)²+(y)²+(2√2z)²+(2×(−√2x)×y)+(2×y×2√2z)+(2×2√2z ×(−√2x))

 

=(−√2x+y+2√2z)²

 

Identity used:

[a²+b²+c²+2ab+2bc+2ca = (a²+b²+c²)]

 

=(−√2x+y+2√2z) (−2√x+y+2√2z)

 

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