Question

10. Factorise:
2x2 + y2 + 8z2 – 2V2 xy + 4V2 yz – 8xz​

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.

----------------------------------------------------------------------------------------------------

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)