Factorise:(i) 4x² + 9y² + 16z² + 12xy – 24yz – 16xz(ii) 2x² + y² + 8z² – 2√2xy + 4√2yz – 8xz

Question

KnowledgeBoat · Accepted Answer

(i) 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 [∵ (x + y + z)² = x² + y² + z² + 2xy + 2yz + 2zx] Hence, 4x² + 9y² + 16z² + 12xy - 24yz - 16xz = (2x + 3y - 4z)(2x + 3y - 4z) (ii) 2x² + y² + 8z² - xy + yz - 8xz [∵ (a + b + c)² = (a)² + (b)² + (c)² + 2ab + 2bc + 2ca] Hence, 2x² + y² + 8z² -xy + yz - 8zx = (-x + y + z)(-x + y + z)

Mathematics

Factorise:(i) 4x² + 9y² + 16z² + 12xy – 24yz – 16xz(ii) 2x² + y² + 8z² – 2√2xy + 4√2yz – 8xz

Polynomials

Related Questions

Evaluate the following using suitable identities:
(i) (99)³
(ii) (102)³
(iii) (998)³

Mathematics

Factorise:(i) 4x² + 9y² + 16z² + 12xy – 24yz – 16xz(ii) 2x² + y² + 8z² – 2√2xy + 4√2yz – 8xz

Polynomials

Related Questions

Evaluate the following using suitable identities:(i) (99)3(ii) (102)3(iii) (998)3

Evaluate the following using suitable identities:
(i) (99)³
(ii) (102)³
(iii) (998)³