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4x 2 + 9y 2 + 16z 2 + 12xy - 24yz - 16xz 4x 2 + 9y 2 + 16z 2 + 12xy - 24yz - 16xz = (2x) 2 + (3y) 2 + (- 4z) 2 + 2(2x) (3y) + (3y) (- 4z) + (- 4z) (- 2x) = {2x + 3y) + (- 4z)} 2 = (2x + 3y - 4z) 2 = (2x + 3y - 4z) (2x + 3y - 4z)

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Polynomials

Short Answer Type

191. Factorise

4x² + 9y² + 16z² + 12xy - 24yz - 16xz

4x² + 9y² + 16z² + 12xy - 24yz - 16xz
4x² + 9y² + 16z² + 12xy - 24yz - 16xz
= (2x)² + (3y)² + (- 4z)² + 2(2x) (3y) + (3y) (- 4z) + (- 4z) (- 2x)
= {2x + 3y) + (- 4z)}² = (2x + 3y - 4z)²
= (2x + 3y - 4z) (2x + 3y - 4z)