Question

Factorize
4x^2-4xy+y^2-9z2
16-x^2-2xy-y^2​

Answer 1

Answer:

(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)

Answer 2

Step-by-step explanation:

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