Question

factorise 4x²+9y²+16z²+12xy-24yz-16xz​

Answer 1

Answer:

Question :-

➠ 4x² + 9y² + 16z² + 12xy - 24yz - 16xz

Formula used :-

➪ a² + b² + c² + 2ab + 2bc + 2ca

➭ (a + b + c)²

Answer :-

➠ 4x² + 9y² + 16z² + 12xy - 24yz - 16xz

➻ (2x)² + (3y)² + (- 4z)² + 2 × 2x × 3y + 2 × 3y × (- 4z) + 2 × (- 4z) × (2x)

➻ (2x + 3y - 4z)²

➻ (2x + 3y - 4z) (2x + 3y - 4z)

∴ The value of 4x² + 9y² + 16z² + 12xy - 24yz - 16xz is

(2x + 3y - 4z) (2x + 3y - 4z)

Answer 2

*Here is your answer:-

Solution:-

4x² + 9y² + 16z² – 12xy – 24yz + 16xz

• = (2x)² + (–3y)² + (4z)³ + 2(2x)(–3y) +2(–3y)(4z) + 2 (4z)(2x)

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

• = (2x)² + (–3y)² + (4z)³ + 2(2x)(–3y) + 2 (–3y) (4z) + 2 (4z) (2x)

• = (2x – 3y + 4z)²

Hence,

• (2x - 3y + 4z)²